Probabilistic earth model for subterranean fracture simulation

ABSTRACT

Systems, methods, and instructions encoded in a computer-readable medium can perform operations related to generating a model of a subterranean formation based on a probabilistic earth model. An earth model including a probability distribution for a property of a subterranean region is received. A subterranean formation model is generated based on sampling the probability distribution for the property. The subterranean formation model includes information on boundaries of rock blocks of a formation in the subterranean region. The subterranean formation model may be used for simulating an injection treatment applied to the formation, for example, to predict fracture propagation in the formation. In some implementations, the subterranean formation model may be used for designing an injection treatment for the formation.

BACKGROUND

Oil and gas wells produce oil, gas and/or byproducts from subterraneanpetroleum reservoirs. Petroleum reservoirs, such as those containing oiland gas, typically include finite-dimensional, discontinuous,inhomogeneous, anisotropic, non-elastic (DIANE) rock formations. Suchformations, in their natural state (prior to any fracture treatment),typically include natural fracture networks. Natural fracture networkscan include fractures of various sizes and shapes, as well as sets offractures having different orientations.

During a fracture treatment, fluids are pumped under high pressure intoa rock formation through a well bore to artificially fracture theformations and increase permeability and production from the formation.Fracture treatments (as well as production and other activities) cancause complex fracture patterns to develop within the natural fracturepattern in the formation. Complex-fracture patterns can include complexnetworks of fractures that extend to the well bore, along multipleazimuths, in multiple different planes and directions, alongdiscontinuities in rock, and in multiple regions of a reservoir.

SUMMARY

Systems, methods, and instructions encoded in a computer-readable mediumcan perform operations related to generating a model of a subterraneanformation based on a probabilistic earth model. In one general aspect, aprobabilistic earth model for a subterranean region is used to predictrock block boundaries for a formation in the subterranean region.

In one aspect, an earth model is received. The earth model includes aprobability distribution for a property of a subterranean region. Asubterranean formation model is generated based on sampling theprobability distribution. The subterranean formation model includesinformation on boundaries of multiple rock blocks of a formation in thesubterranean region.

Implementations may include one or more of the following features. Thesubterranean formation model is used as an input for a simulation offracture propagation in the subterranean formation. The simulation offracture propagation predicts, for each of the rock blocks, a responseof the rock block to forces acting on the rock block during an injectiontreatment for the subterranean formation. The simulation of fracturepropagation generates an output subterranean formation model includinginformation on an updated boundary of at least one of the rock blocks.The earth model includes information on sizes of rock formations in thesubterranean region, shapes of rock formations in the subterraneanregion, locations of rock formations in the subterranean region, and/ormineral compositions of rock formations in the subterranean region. Theearth model includes information on hydrocarbon reservoirs in thesubterranean region. The probability distribution includes values forthe property and a probability for each of the values. Sampling theprobability distribution includes randomly selecting one of the values.The information on the boundaries of the rock blocks is based on thesampling. The property relates to a fracture dip angle, a fracturedirection, a fracture shape, a fracture aperture, a fracturepersistence, a fracture length, a fracture location, a fracture density,and/or a fracture spacing. The earth model includes information onlateral discontinuities within a rock layer of the subterranean region,vertical discontinuities forming multiple rock layers in thesubterranean region, a primary orientation of fracture sets in thesubterranean region, a secondary orientation of fracture sets in thesubterranean region, and/or properties of formation materials in thesubterranean region. Additional subterranean formation models aregenerated based on additional sampling of the probability distribution.Each additional subterranean formation model includes additionalinformation on boundaries of rock blocks based on the additionalsampling. The probability distribution is a first probabilitydistribution, and the earth model includes additional probabilitydistributions for additional properties of the subterranean region.Generating the subterranean formation model includes sampling the firstprobability distribution and sampling each additional probabilitydistribution. The injection treatment is a fracture treatment.

In one aspect, an earth model for a subterranean region is received. Theearth model includes a probability distribution for a property of thesubterranean region. Data processing apparatus generates a subterraneanformation model based on sampling the probability distribution. Thesubterranean formation model includes elements that represent rockblocks of a subterranean formation in the subterranean region. Eachelement includes information on boundaries of at least one of the rockblocks.

Implementations may include one or more of the following features. Theearth model is generated based on data from an outcrop in thesubterranean region, microseismic data from the subterranean region,seismic data from the subterranean region, pressure transient data fromthe subterranean region, and/or open hole logging of a well bore in thesubterranean region. The subterranean formation model is used to predictcomplex fractures in the subterranean formation. The complex fracturesinclude fractures that extend along multiple azimuths in thesubterranean formation, fractures that extend in multiple planes in thesubterranean formation, fractures that extend in multiple directions inthe subterranean formation, and/or fractures that intersect each otherin the subterranean formation. The subterranean formation model is afirst subterranean formation. Additional subterranean formation modelsare generated based on sampling the probability distribution for theproperty. The first subterranean formation model and each additionalsubterranean formation model are used as input subterranean formationmodels for simulating an injection treatment in the subterraneanformation. The simulating generates an output subterranean formationmodel for each of the input subterranean formation models. Theprobability distribution is generated by using microseismic data torefine an initial probability distribution for the subterranean region.The subterranean formation includes a formation material, and the earthmodel includes information on a porosity of the formation material, apermeability of the formation material, a mineral composition of theformation material, a coefficient of friction of the formation material,a Young's modulus of the formation material, a Poisson's ratio of theformation material, a compressibility of the formation material, afracture toughness of the formation material, a cohesive strength of theformation material, a Biot's constant of the formation material, and/ora pressure of fluids resident in the formation material.

In one aspect, a system for performing an injection treatment includesan injection treatment control subsystem. The injection treatmentcontrol subsystem is adapted to control an injection treatment appliedto a subterranean formation in a subterranean region through a well boredefined in the subterranean formation. The injection treatment is basedon a simulation of the injection treatment in a subterranean formationmodel. The subterranean formation model includes information onboundaries of rock blocks of the subterranean formation. Thesubterranean formation model is generated based on sampling aprobability distribution included in an earth model for the subterraneanregion.

Implementations may include one or more of the following features. Thesystem includes a computing subsystem that performs the simulation. Thesystem includes a tool installed in the well bore. The tool is adaptedto inject treatment fluid into the subterranean formation based oninformation received from the injection treatment control subsystem. Thesystem further includes the subterranean formation. The subterraneanformation includes shale, sandstone, carbonates, and/or coal. The wellbore includes a horizontal well bore. Controlling the injectiontreatment includes controlling at least one of a flow rate, a flowvolume, an injection location, a fluid property, a proppant property, ora slurry concentration.

In one aspect, a model is generated. The model includes information onboundaries of rock blocks of a subterranean formation in a subterraneanregion. The model is generated based on sampling a probabilitydistribution for a property of the subterranean region. An injectiontreatment is designed for the subterranean formation based on simulatingfracture propagation in the model. The injection treatment is applied tothe subterranean formation through a well bore in the subterraneanformation.

Implementations may include one or more of the following features.Applying the injection treatment includes injecting treatment fluid intothe subterranean formation at an injection pressure less than a fractureinitiation pressure for the subterranean formation, injecting treatmentfluid into the subterranean formation at an injection pressure greaterthan or equal to a fracture initiation pressure for the subterraneanformation, injecting treatment fluid into the subterranean formation atan injection pressure less than a fracture closure pressure for thesubterranean formation, and/or injecting treatment fluid into thesubterranean formation at an injection pressure greater than or equal toa fracture closure pressure for the subterranean formation. Applying theinjection treatment initiates a fracture in the subterranean formation.Applying the injection treatment dilates a natural fracture in thesubterranean formation. The injection treatment includes a pad phase ofa fracture treatment and/or a proppant-laden phase of a fracturetreatment. The simulating generates an output model that includesupdated boundaries for the rock blocks. Designing the injectiontreatment includes using the output model to simulate production ofresources from the subterranean formation.

DESCRIPTION OF DRAWINGS

FIG. 1A is a diagram of an example well system.

FIG. 1B is a diagram of the example treatment well 102 of FIG. 1A.

FIG. 1C is a diagram of the example computing device 110 of FIG. 1A.

FIG. 1D is a diagram of an example well system.

FIG. 2A is a plot of nine example fracture patterns.

FIGS. 2B and 2C are plots of the nine example fracture patterns of FIG.2A, with microseismic data overlaid on each fracture pattern.

FIG. 3A shows an example population distribution for an example fractureparameter.

FIG. 3B shows an example initial sample distribution for an examplefracture parameter.

FIG. 3C shows an example refined population distribution for an examplefracture parameter.

FIG. 4A is a diagram of an example model of discrete rock blocks of asubterranean formation.

FIGS. 4B and 4C are diagrams of example movements of the discrete rockblocks of the subterranean formation of FIG. 4A.

FIG. 5 shows an example screen shot of a software tool for simulatingfracture propagation in a subterranean formation.

FIG. 6A is a flow chart of an example technique for refining aprobability distribution of subterranean fracture properties.

FIG. 6B is a flow chart of an example technique for simulating complexfracture propagation in a subterranean formation.

FIG. 7A is a flow chart of an example technique for fitting microseismicevent data.

FIG. 7B is a flow chart of an example technique for generating aprobability distribution.

FIG. 7C is a flow chart of an example technique for generating aprobability distribution.

Like reference symbols in the various drawings indicate like elements.

DETAILED DESCRIPTION

FIG. 1A is diagram of an example well system 100. The example wellsystem 100 includes a treatment well 102 and an observation well 104.The observation well 104 can be located remotely from the treatment well102. The well system 100 can include one or more additional treatmentwells and/or one or more additional observation wells. The well system100 can include a computing subsystem 110, which may include one or morecomputing devices located at one or more well sites and/or at one ormore remote locations. The computing subsystem 110 may analyzemicroseismic data, seismic data, fracture data, and/or other types ofdata collected from a subterranean region. The computing subsystem 110may predict and/or simulate fractures and fracture networks in asubterranean formation. The predicted and/or simulated fractures mayinclude natural fracture patterns, propagated and/or complex fracturenetworks, and others. The computing subsystem 110 may simulate aninjection treatment and/or resource production for a subterraneanformation. In some implementations, the computing subsystem 110simulates behavior of finite-dimensional, discontinuous, inhomogeneous,anisotropic, non-elastic (DIANE) rock formations during an injectiontreatment.

The example treatment well 102 includes a well bore 101 beneath thesurface 106, in a subterranean region 121. The region 121 may include anatural fracture network 108 that extends through one or moresubterranean formations in the region 121. The natural fracture network108 may define multiple rock blocks 115 in one or more rock formations.The rock blocks 115 can range in size from centimeters, or smaller, insize to hundreds of meters, or larger, in size. The example treatmentwell 102 includes an injection treatment subsystem 120, which includesinstrument trucks 116, pump trucks 114, and other equipment that may beused to control an injection treatment applied to the subterraneanformation through the well bore 101. In some implementations, thetreatment well 102 is used to apply an injection treatment to and/orextract resources from the subterranean formation through the well bore101.

Properties of the injection treatment can be calculated and/or selectedbased on computer simulations of complex fracture propagation in thesubterranean region 121. For example, the computing subsystem 110 caninclude a fracture simulation system that predicts the behavior ofdiscrete rock blocks 115 in the subterranean region 121 by simulatingforces applied to each individual rock block. The simulations mayrepresent the boundaries and/or locations of the rock blocks using asubterranean formation model defined in memory. The subterraneanformation model may include a geometric model the represents theboundaries of the rock blocks; the subterranean formation model mayinclude additional information regarding the subterranean formation. Thesimulations can include probabilistic simulations that generate a rangeof output subterranean formation models based on multiple inputsubterranean formation models. Each subterranean formation input modelcan be generated by randomly sampling a probabilistic earth model thatdescribes the subterranean region. In some implementations, theprobabilistic earth model and/or probability distributions included inthe earth model are developed or refined based on microseismic data.

As shown in FIG. 1A, the observation well 104 includes a well bore 111in a subterranean region beneath the surface 106. The observation well104 includes sensors 112 and other equipment that can be used to sensemicroseismic information. The sensors 112 may include geophones and/orother types of listening equipment. The sensors 112 can be located at avariety of positions in the well system 100. In FIG. 1A, the examplesensors are installed beneath the surface 106 in the well bore 111. Insome implementations, sensors may additionally or alternatively bepositioned in other locations above or below the surface 106; in otherlocations within the well bore 111 and/or within another well bore,and/or in other locations in the well system 100. The observation well104 may include additional equipment (e.g., working string, packers,casing, and/or other equipment) not shown in FIG. 1A. In someimplementations, microseismic data is detected by sensors installed inthe treatment well 102 and/or at the surface 106, without use of anobservation well.

Microseismic information detected at the well bore 111 can includeacoustic signals generated by an injection treatment applied through thetreatment well 102 or another treatment well (not shown), acousticsignals generated by drilling and/or production activities at thetreatment well 102 or another well, acoustic signals generated bynaturally-occurring microseisms in the fracture network 108 and/oranother fracture network (not shown), and/or other acoustic signals. Themicroseismic data can include information on the locations of rockslips, rock movements, rock fractures and/or other events in the wellsystem 100.

The microseismic data can be used to refine or improve knowledge of thefracture network 108 and/or another fracture network. For example,microseismic data based on microseismic events in a first formation,region, or zone can be used to infer properties of a differentformation, region, or zone. In some cases, the fracture simulationsystem uses the microseismic data to refine and/or improve a prioriknowledge of a fracture network. The refined and/or improved knowledgecan then be incorporated into a probabilistic earth model for simulatingcomplex fracture propagation. The simulations can be used to design aninjection treatment applied to a subterranean region. For example, thesimulations can be used to calculate, refine, optimize, improve, orotherwise select parameters, setting, and/or conditions of an injectiontreatment applied to the subterranean formation through the treatmentwell 102.

In some implementations, the computing subsystem 110 can use adiscontinuum model to simulate complex fracture propagation. In someinstances of a discontinuum model, subterranean formations, includingsandstones, carbonates, shales, coals, mudstones, granites, and othermaterials, can be modeled as a collection of discrete rock blocksseparated by fractures, fissures, faults, and/or joints. In some cases,simulations are improved by modeling the rock as a collection ofdiscrete elements and by simulating forces applied to each individualrock block. In some simulations, each rock block can translate, rotate,and/or fracture, for example, as a result of the simulated forces actingon the rock blocks. The simulated forces may include, for example,forces caused by motion of the rock blocks, normal and shear forces dueto contact between rock blocks, forces caused by fluid flow between rockblocks, pressure of resident fluids in the rock blocks, and/or otherforces. The discontinuum model can be used to simulate fracturedilation, fracture propagation, tensile fractures, open fractures formedby shear displacements along rock-block boundaries, and/or other typesof phenomena.

An example discontinuum model technique that can be used to simulatecomplex fracture propagation in a subterranean formation is thediscontinuous deformation analysis (DDA) technique and variationsthereof. According to the DDA technique, tensile fracture propagationcan be modeled along with open fractures resulting from sheardisplacement of the rock blocks. DDA does not require symmetry of therock blocks or symmetrical fracture propagation. That is to say, in someimplementations, any fracture pattern can be set into the formation, andfracture growth and/or complex fracture propagation can form fracturepatterns that are asymmetrical about any point, plane, or axis in theformation. For example, FIG. 4A shows a model of a simple rock formation400 a that includes seven discrete rock blocks separated by fracturesthat are asymmetrical. Another example discontinuum model technique thatcan be applied to modeling complex fracture propagation in asubterranean formation is the numerical manifold method (NMM) andvariations thereof. In some implementations, an NMM technique couplesfeatures of a discontinuum discrete element method with features of acontinuum analysis.

In some implementations, the discontinuum model can achieve one or moreadvantages. For example, the discontinuum model can simulatemultiple-fracture propagation, including multiple asymmetric fractures,hydraulic fractures, and others. Such simulations can simulateasymmetric complex fracture patterns and multiple asymmetric planarfractures propagating from multiple entry points along a well bore(e.g., a vertical well bore, a horizontal well bore, and/or a well borehaving deviations at any angle). The discontinuum model can simulatedilating complex fracture networks, opening and closing of fracturescaused by shear displacement of rock blocks along cleavage planes,and/or other effects. In addition, in various implementations, thediscontinuum model can simulate fracture propagation in formationshaving anisotropic rock properties; the discontinuum model can simulatechanges in a stress field resulting from pore pressure depletion andfracturing; the discontinuum model can simulate fracture reorientationin response to changes in the stress field or fracturing conditions;and/or the discontinuum model can predict residual fracture widthcreated by shear offset of rock blocks. The discontinuum model cansimulate initiation and propagation of fractures in multiple directionsand/or orientations from a single injection location. For example, thediscontinuum model can simulate initiation and growth of a two fracturesin two different directions from a single injection location, and thetwo fractures may initiate and grow in planes separated by an arbitraryangle (e.g., any angle between zero and 360 degrees, and/or in anotherrange of directions). The directions of the fractures may be influencedby primary and secondary fracture orientations in the formation.

In some implementations, the computing subsystem 110 can perform aprobabilistic simulation of complex fracture propagation in thesubterranean formation. The complex fracture network that hydraulicfracturing could dilate, propagate, and/or connect typically depends onthe well location and the connectivity of the initial fracture network.In some implementations, probabilistic techniques simulate fracturepropagation in multiple different initial fracture network models togenerate a range of possible outputs. For example, initial fracturenetwork models can be generated by randomly sampling probabilitydistributions of fracture parameters. Complex fracture propagation canbe simulated in each of the initial fracture network models to generatemultiple different output fracture models. The simulations can model thesubterranean formation as a collection of rock blocks, and predictcomplex fractures generated by forces applied to the rock blocks. Incontrast to a deterministic technique that predicts a single outcome, aprobabilistic technique can account for uncertainty in formationproperties by generating a range of possible outcomes based on a rangeof possible formation properties. The range of outcomes can, in turn, beused to generate output probability distributions that describepredicted properties of a complex fracture network and/or otherinformation.

Monte Carlo simulation techniques are an example technique forperforming probabilistic numerical simulations. In a typical Monte Carlosimulation, input values of one or more variables are randomly selectedby sampling a probability distribution for each variable. In aprobabilistic simulation of subterranean complex fracture propagation,the randomly sampled variables may include, for example, fracture dip,fracture direction, fracture persistence, fracture aperture, fracturetrace length, fracture spacing, fracture density, stress anisotropy,coefficient of friction between rock blocks, natural fracture roughness,and others. Some or all of these example variables and/or othervariables can be described by a probability distribution and randomlysampled. For each set of input values, the Monte Carlo simulationprovides a single output, and a range of outputs are obtained based onthe multiple sets of input values. The outputs can be used to predictcharacteristics of complex fracture growth in the subterranean formationmodeled by the simulations and/or other types of information.

In some implementations, the computing subsystem 110 can use aprobabilistic earth model to populate a geometric model of asubterranean formation, and the geometric model can be used as an inputfor simulating complex fracture propagation in the subterraneanformation. For example, the probabilistic earth model can be used togenerate multiple realizations of input geometric models fordiscontinuum simulations, and the output models from the discontinuumsimulations can be analyzed collectively and/or individually.

In many underground petroleum reservoirs, properties of the discreterock blocks and characteristics of discontinuities are known with someuncertainty. For example, the exact pattern of fractures, faults,fissures, and other features, existing in the reservoir are typicallynot known with certainty, and probability distributions for thediscontinuities can be generated based on data from analog fields,outcrop mapping, open hole logging, microseismic data, and/or otherinformation. The uncertainty may result from imprecise or incompleteknowledge of the rock properties, inhomogeneity of the rock properties,and/or other sources of uncertainty. Uncertainty in the properties ofthe rock blocks and characteristics of the discontinuities can beaccounted for in numerical simulations of the fracture network bydefining a probabilistic earth model. The probabilistic earth model,which includes probability distributions that describe ranges of valuesfor each input variable (and a probability for each value), can be usedto populate geometric models that serve as an inputs for probabilisticsimulations of complex fracture growth.

A probabilistic earth model can describe, among other things,discontinuities in a subterranean region. For example, thediscontinuities can include discontinuities at any orientation,including lateral discontinuities that create rock blocks in a singlelayer, vertical discontinuities that create a multilayer system ofreservoir rocks, fracture sets having a primary orientation, fracturesets having a secondary orientation, and/or others. In some cases, somediscontinuities are known with reasonable certainty, for example, majorfaults can be mapped through a formation with more certainty than someother types of features. In some cases, open hole logging can identifychanges in lithology that create vertical discontinuities. In somecases, major faults can be mapped using microseismic data, pressuretransient data, and/or other types of data. Properties of otherdiscontinuities, for example, natural fractures or fissures, may not beknown with as much certainty as the major faults.

In some implementations, using a probabilistic earth model to populate ageometric model for complex fracture simulation can be used to achieveone or more advantages. For example, a probabilistic earth model mayallow for both lateral discontinuities and vertical discontinuities tobe included in the geometric model. The lateral discontinuities mayrepresent, for example, lateral and vertical changes in lithology aswell as fracture discontinuities, fissures, and faults. A probabilisticearth model may allow complex rock geometries (e.g., lenticular rockgeometries, etc.) to be included in the geometric model used for complexfracture simulation. A probabilistic earth model may allow modeling of“stacked” reservoirs, i.e., multiple reservoirs separated vertically bychanges in lithology. A probabilistic earth model may describe rocklayers that “pinch out” between well bores, which may include rocklayers separated by impermeable materials. A probabilistic earth modelcan be used as an input for Monte Carlo and other types of probabilisticsimulation.

In some implementations, the computing subsystem 110 can usemicroseismic data to refine initial probability distributions describingproperties of natural fractures and patterns in the subterraneanformation. For example, initial probability distributions can be refinedby comparing stochastically generated fracture patterns to observedmicroseismic events recorded during fracturing, during injection belowfracture propagation pressure, during production, and/or at other times.In this manner, fracture modeling, pumping or production operations, andmicroseismic mapping can be linked to predict fracture patterns in otherlocations.

Fluid injection, production, and other activities can createmicroseismic events in a subterranean formation, and microseismic datacan be collected from the subterranean formation. The locations ofindividual microseismic events can be determined based on themicroseismic data, and the locations can be matched with numericallysimulated fracture patterns. Each numerically simulated fracture patterncan be generated based on a set of fracture parameters, and values forone or more of the parameters may be selected by randomly samplinginitial probability distributions for the parameter. Identifyingsimulated fracture patterns that match the microseismic data allows theinitial probability distributions to be refined or corrected for thenext location where the process (i.e., the fracture or productionprocess) is to be implemented. The probability distributions mayrepresent variables such as, for example, fracture dip, fracturedirection, fracture persistence, fracture dimension, fracture shape,fracture density, fracture aperture, fracture trace length, fracturespacing, and/or others.

In some instances, the initial probability distributions are genericprobability distributions for a certain type of formation, material, orregion. The generic probability distributions can be refined for aparticular geographic area, formation, field, layer, etc. by simulatingfracture patterns based on the generic probability distributions andselecting the simulated fracture patterns that match microseismic datafrom the particular geographic area, formation, field, layer, etc. Therefined probability distributions can be subsequently used for otherlocations in the same geographic area, formation, field, layer, etc. topredict natural fracture patterns. As more microseismic events arerecorded and mapped, the probability distributions can be furtherrefined, for example, in an iterative or another fashion.

In some cases the matching technique (i.e., matching microseismic datato simulated fracture patterns) can be done in real-time as events arerecorded, or the matching technique can be implemented based onpreviously recorded microseismic data. After mismatches of microseismicevents and simulated fracture patterns are eliminated, the remaining“matched” maps of microseismic events and natural fracture modelrealizations can be used to regenerate and/or refine the probabilitydistributions. The regenerated or refined probability distributions ofnatural fracture properties and patterns can then be used to predictnatural fracture patterns at other locations.

FIG. 1B is a diagram showing an example injection treatment applied atthe example treatment well 102 of FIG. 1A. As shown in FIG. 1B, thetreatment well 102 intersects a subterranean formation 122. In someimplementations, the formation 122 includes naturally fractured rockcontaining oil, gas, and/or other resources. For example, the formation122 may include fractured sandstone, fractured carbonate materials,fractured shale, fractured coal, fractured mudstone, fractured granite,and/or others fractured material. In some implementations, the treatmentwell 102 intersects other types of formations, including reservoirs thatare not naturally fractured to any significant degree.

As shown in FIG. 1B, an injection treatment can be applied to thesubterranean formation 122 through the well bore 101. The injectiontreatment may include a fracture treatment and/or another type ofstimulation treatment. A fracture treatment may include a mini fracturetest treatment, a regular or full fracture treatment, a follow-onfracture treatment, a re-fracture treatment, a final fracture treatmentand/or another type of fracture treatment. The injection treatment mayinject treatment fluid into the formation above, at or below a fractureinitiation pressure for the formation, above at or below a fractureclosure pressure for the formation, and/or at another fluid pressure.Fracture initiation pressure refers to a minimum fluid injectionpressure that can initiate and/or propagate artificial fractures in thesubterranean formation. As such, application of an injection treatmentmay or may not initiate and/or propagate artificial fractures in theformation. Fracture closure pressure refers to a minimum fluid injectionpressure that can dilate existing fractures in the subterraneanformation. As such, application of an injection treatment may or may notdilate natural and/or artificial fractures in the formation.

The injection treatment and/or properties of the injection treatment maybe calculated, improved, optimized, and/or otherwise selected based onsimulations (e.g., computer-implemented simulations) of complex fracturepropagation in the formation 122 or another formation. For example, theinjection treatment may include a flow rate, a flow volume, a slurryconcentration, and/or other characteristics that have been selectedbased on numerical simulations of a injection treatment applied to theformation 122. A simulated complex fracture network may be used topredict a volume, rate, and/or location of resource production from theformation 122.

The example treatment well 102 shown in FIG. 1B includes the well bore101, a casing 103 and well head 113. The well bore 101 shown in FIG. 1Bincludes a vertical well bore. More generally, a treatment well mayadditionally or alternatively include one or more slant well bores, oneor more horizontal well bores, one or more deviated well bores, and/orother types of well bores. The casing 103 may be cemented or otherwisesecured in the well bore 101. Perforations 109 may be formed in thecasing 103 in the formation 122 to allow treatment fluids, proppants,and/or other materials to flow into the formation 122, and/or to allowoil, gas, by-products, and other materials to flow into the treatmentwell 102 and be produced to the surface 106. Perforations 109 may beformed using shape charges, a perforating gun, and/or other tools.

As shown in FIG. 1B, a working string 107 is disposed in the well bore101. The working string 107 may include coiled tubing, sectioned pipe,and/or other types of tubing and/or pipe. As shown in FIG. 1B, afracturing tool 119 is coupled to the working string 107. The fracturingtool 119 can include a hydrajetting/fracturing tool and/or another typeof fracturing tool. Example hydrajetting/fracturing tools include theSURGIFRAC tool (manufactured by HALLIBURTON), the COBRA FRAC tool(manufactured by HALLIBURTON), and others. The packers 105 shown in FIG.1B seal the annulus of the well bore 101 above and below the formation122. Packers 105 may include mechanical packers, fluid inflatablepackers, sand packers, and/or other types of packers.

As shown in FIG. 1B, the pump trucks 114 are coupled to the workingstring 107 at the surface 106. The pump trucks 114 may include mobilevehicles, immobile installations, skids, hoses, tubes, fluid tanks orreservoirs, pumps, valves, and/or other suitable structures andequipment. During operation, the pump trucks 114 pump fluid 117 to thefracturing tool 119, which performs the injection treatment by injectingthe fluid 117 into the formation 122. The fluid 117 may include a pad,proppants, a flush fluid, additives, and/or other materials. Forexample, a injection treatment may include a pad phase, where a pad(which typically includes fluids without proppants), is pumped down thewell bore and injected into the surrounding the formation to inducefracture. After the pad phase, the injection treatment may include asubsequent proppant phase, where fracturing fluids containing proppantsare pumped into the formation. The injected proppants may hold thefractures open to stimulate production from the formation. After theproppant phase, a clear fluid flush may be pumped into the well bore toclean the well bore of proppants and/or other materials.

As shown in FIG. 1B, the instrument trucks 116 are also provided at thesurface 106. The instrument trucks 116 may include mobile vehicles,immobile installations, and/or other suitable structures. The instrumenttrucks 116 may include a technical command center. The exampleinstrument trucks 116 include a injection control system that monitorsand controls the injection treatment. The injection control system maycontrol the pump trucks 114, fracturing tool 119, fluid valves, and/orother equipment used to apply the injection treatment and/or aperforating treatment. The treatment well 102 may also include surfaceand down-hole sensors (not shown) to measure pressure, rate, temperatureand/or other parameters of treatment and/or production. The treatmentwell 102 may include pump controls and/or other types of controls forstarting, stopping and/or otherwise controlling pumping as well ascontrols for selecting and/or otherwise controlling fluids pumped duringthe injection treatment. The injection control system in the instrumenttrucks 116 can communicate with the surface and/or subsurface sensor,instruments, and other equipment to monitor and control the injectiontreatment.

The example instrument trucks 116 shown in FIG. 1B communicate with thepump truck 114, the surface and subsurface instruments, the computingsubsystem 110, and/or other systems and subsystems through one or morecommunication links 118. All or part of the computing system 110 may becontained in the instrument trucks 116; all or part of the computingsystem 110 may be contained outside of the instrument trucks at a wellsite and/or at a remote location. In an example embodiment, thecomputing subsystem 110 is contained in a technical command center atthe well site. In another example embodiment, the computing subsystem110 is contained in a real-time operations center at a remote location,and the computing subsystem 110 communicates by satellite with ainjection control system at the well site. In some embodiments, thecomputing subsystem 110, the listening subsystem (which includes thesensors 112), and other subsystems at one or more well sites communicatewith a remote real-time operations center by wide area network.

The communication links 118 can include multiple uncoupled communicationlinks and/or a network of coupled communication links. The communicationlinks 118 may include wired and/or wireless communications systems. Forexample, surface sensors and pump controls may communicate with theinjection control system through a wired or wireless link, down-holesensors may communicate to a receiver at the surface through a wired orwireless link, and the receiver may be coupled by a wired or wirelesslink to the injection control system. As another example, the instrumenttruck 116 may communicate with the pump trucks 114 and/or the computingsubsystem 110 via wired and/or wireless digital data communicationnetworks, wired and/or wireless analog communication links, and/or othertypes of communication links.

The injection control system and/or other components of the instrumenttrucks 116 can communicate with the computing subsystem 110 to receiveinjection treatment parameters and/or other information. The computingsubsystem 110 may include a fracture simulation system that calculates,selects, and/or optimizes injection treatment parameters for treatmentof the formation 122 or another formation. The example fracturesimulation system implemented by the computing subsystem 110 in FIG. 1Bcan simulate the injection treatment during a design phase of theinjection treatment. The fracture simulation system can use datacollected during a injection treatment to simulate further injectiontreatments in the formation 122 and/or other formations. The fracturesimulation system can be updated during and after a injection treatmentbased on measured and/or observed data, including fracture, subsequentproduction and/or other data.

In one aspect of operation, the fracturing tool 119 is coupled to theworking string 107 and positioned in the treatment well 102. The packers105 are set to isolate the formation 122. The pump trucks 114 pump fluid117 down the working string 107 to the fracturing tool 119. The fluid117 exits the fracturing tool 119 and fractures the formation 122. Insome implementations, the fluid may include a fluid pad pumped down thetreatment well 102 until breakdown of the formation 122, and proppantsmay then be pumped into the fractures, followed by a fluid flush. Insome implementations, the injection treatment is performed in adifferent manner.

Some embodiments and/or some aspects of the techniques and operationsdescribed herein may be implemented by a computing subsystem configuredto provide the functionality described. In various embodiments, acomputing device may include any of various types of devices, including,but not limited to, a personal computer system, desktop computer,laptop, notebook, mainframe computer system, handheld computer,workstation, network computer, application server, storage device, orany type of computing or electronic device.

FIG. 1C is a diagram of the example computing subsystem 110 of FIG. 1A.The example computing subsystem 110 can be located at or near one ormore wells of the well system 100 and/or at a remote location. Theexample computing subsystem 110 includes a processor 160, a memory 150,and input/output controllers 170 communicably coupled by a bus 165. Thememory can include, for example, a random access memory (RAM), a storagedevice (e.g., a writable read-only memory (ROM) and/or others), a harddisk, and/or another type of storage medium. The computing subsystem 110can be preprogrammed and/or it can be programmed (and reprogrammed) byloading a program from another source (e.g., from a CD-ROM, from anothercomputer device through a data network, and/or in another manner). Theinput/output controller 170 is coupled to input/output devices (e.g., amonitor 175, a mouse, a keyboard, and/or other input/output devices) andto a network 180. The input/output devices receive and transmit data inanalog or digital form over communication links such as a serial link,wireless link (e.g., infrared, radio frequency, and/or others), parallellink, and/or another type of link.

The network 180 can include any type of data communication network. Forexample, the network 180 can include a wireless and/or a wired network,a Local Area Network (LAN), a Wide Area Network (WAN), a privatenetwork, a public network (such as the Internet), a WiFi network, anetwork that includes a satellite link, and/or another type of datacommunication network. The network 180 can include some or all of thecommunication link 118 of FIG. 1A.

The memory 150 can store instructions (e.g., computer code) associatedwith an operating system, computer applications, and/or other resources.The memory 150 can also store application data and data objects that canbe interpreted by one or more applications and/or virtual machinesrunning on the computing subsystem 110. As shown in FIG. 1C, the examplememory 150 includes microseismic data 151, probability data 152,fracture data 153, treatment data 154, other data 155, and applications156. In some implementations, a memory of a computing device may includesome or all of the information stored in the memory 150.

The microseismic data 151 can include information on the locations ofmicroseisms in a subterranean formation. For example, the microseismicdata can include information based on acoustic data detected at theobservation well 104, at the surface 106, at the treatment well 102,and/or at another location. The microseismic data 151 can be matched tosimulated fracture patterns in order to refine an initial distributionof fracture properties. For example, a map of the locations of themicroseismic events can be compared to a map of a simulated fracturepattern to identify whether the simulated fracture pattern accuratelyrepresents the measured microseismic data. Example microseismic data isrepresented in the graphical user interface in FIG. 5.

The probability data 152 can include probability distributions forparameters used in numerical simulations of fracture patterns andcomplex fracture propagation in a subterranean formation. Theprobability data 152 may be included in a probabilistic earth model. Aprobability distribution for a given parameter typically includes one ormore possible values (or one or more possible ranges of values) for thegiven parameter and the likelihood of occurrence for each possible value(or each possible range of values). The probability data 152 can includegeneric probability distributions for a certain type of formation,material, or region. An example generic probability distribution isshown in FIG. 3A and discussed below. The probability data 152 caninclude initial sample probability distributions for a particularformation, material, or region. An example initial sample probabilitydistribution is shown in FIG. 3B and discussed below. The probabilitydata 152 can include refined probability distributions that have beenmodified to represent a particular geographic area, formation, field,layer, etc., for example, by matching microseismic data from theparticular geographic area, formation, field, layer, etc. with simulatedfracture patterns. An example refined probability distribution is shownin FIG. 3C and discussed below. The probability data 152 can includeoutput probability distributions representing the output of aprobabilistic simulation of complex fracture propagation in asubterranean formation. For example, the output probability distributionmay be based on complex fracture simulation for multiple differentinitial geometric models.

The fracture data 153 can include information on fractures, fracturepatterns and complex fracture network generated by numericalsimulations. The fracture data 153 may identify the locations, sizes,shapes, and other properties of fractures in a model of a subterraneanformation. In some implementations, the fracture data 153 is representedin a geometric model or another type of construct. For example, ageometric model may represent a subterranean formation as a collectionof rock blocks, and the fractures may be defined with respect to therock blocks. Example fracture data is represented by the naturalfracture patterns shown in FIGS. 2A, 2B, and 2C. Example fracture datais also represented by the geometric models in FIGS. 4A, 4B, and 4C.

The treatment data 154 includes information on injection treatments. Forexample the treatment data 154 can indicate parameters of a previousinjection treatment, parameters of a future injection treatment, and/orparameters of a proposed injection treatment. Such parameters mayinclude information on flow rates, flow volumes, slurry concentrations,fluid compositions, injection locations, injection times, and/or otherparameters. The treatment data 154 can include treatment parameters thathave been optimized and/or selected based on numerical simulations ofcomplex fracture propagation.

The applications 156 can include software applications, scripts,programs, functions, executables, and/or other modules that areinterpreted and/or executed by the processor 160. For example, theapplications 156 can include software applications, scripts, programs,functions, executables, and/or other modules that operate alone or incombination as a fracture simulation system. Such applications mayinclude machine-readable instructions for performing one or more of theoperations shown in FIGS. 6A and 6B. The applications 156, including thefracture simulation system, can obtain input data, such as probabilitydistributions, microseismic data, treatment data, geometric models,and/or other types of input data, from the memory 150, from anotherlocal source, and/or from one or more remote sources (e.g., via thenetwork 180). The applications 156, including the fracture simulationsystem, can generate output data and store the output data in the memory150, in another local medium, and/or in one or more remote devices(e.g., by sending the output data via the network 180).

The processor 160 can execute instructions, for example, to generateoutput data based on data inputs. For example, the processor 160 can runthe applications 156 by executing and/or interpreting the software,scripts, programs, functions, executables, and/or other modulescontained in the applications 156. The processor 160 may perform one ormore of the operations shown in FIGS. 6A and 6B. The input data receivedby the processor 160 and/or the output data generated by the processor160 may include any of the microseismic data 151, the probability data152, the fracture data 153, the treatment data 154, and/or the otherdata 155.

The systems and techniques described with reference to FIGS. 1A, 1B, and1C may be implemented in other types of well systems, using other typesof equipment and apparatus, as appropriate. For example, FIG. 1D showsfeatures of an example embodiment of a well system 190 that includes atreatment well 191 having multiple fluid injection locations in asubterranean region 193 beneath the surface 189. The subterranean region193 includes a fracture network 194 that defines the boundaries anddiscontinuities of rock blocks 195 in a subterranean formation. Theexample treatment well 191 includes a horizontal well bore 192 havingthree fluid injection locations 196 a, 196 b, and 196 c in the fracturenetwork 194. Any number of fluid injection locations may be used. Forexample, a well system may include two, five, tens, hundreds, or anyother number of fluid injection locations. Multiple fluid injectionlocations may also be implemented in other types of well bores and/orother types of well systems, such as, for example, vertical well bores,slant well bores, and/or others.

The treatment well 191 includes an injection treatment subsystem 197that applies injection treatments to the subterranean formation. Theinjection treatment subsystem 197 includes instrument trucks 116, pumptrucks 114, and other features that control the communication oftreatment fluid into the subterranean region 193 through the well bore192. The injection treatment subsystem 197 may include any of thefeatures of the injection treatment subsystem 120 of FIGS. 1A and 1B,and may include fewer, additional, and/or different features. Theinjection treatment subsystem 197 may apply multiple injectiontreatments in succession. For example, the injection treatment subsystemmay treat the subterranean formation in sequence from the toe to theheel of the horizontal well bore 192, and/or in a different sequence inorder to improve or optimize the injection treatment. As a particularexample, the injection treatment subsystem 197 may apply a firstinjection treatment to the formation through the well bore 192 at thefirst injection location 196 a, then apply a second injection treatmentto the formation through the well bore 192 at the second injectionlocation 196 b, and then apply a third injection treatment to theformation through the well bore 192 at the third injection location 196c. The injection treatment subsystem 197 may apply additional injectiontreatments in additional and/or different locations in the same or adifferent order. For example, in some cases, multiple injectiontreatments can be applied simultaneously.

The well system 190 includes sensors 112 at the surface 189. The sensors112 may detect microseismic data during one or more injection treatmentsapplied to the subterranean region 193 through the well bore 192. Thesensors 112 may communicate detected microseismic data to the computingsubsystem 110. The computing subsystem 110 can use the microseismicdata, for example, to identify and/or predict properties of naturalfractures and/or propagated fractures in the fracture network 194. Thecomputing subsystem 110 can simulate, refine, generate, and/or designinjection treatments for the subterranean region 193 based on themicroseismic data and/or based on the properties of the fracture network194 gleaned from the microseismic data. For example, the computingsubsystem 110 may receive microseismic data collected by the sensors 112during a fracture treatment applied at the first injection location 196a, and the computing subsystem 110 may use the microseismic data toidentify properties of natural fractures near the first injectionlocation 196 a and/or to predict properties of natural fractures nearthe second injection location 196 b and/or the third injection location196 c.

In one aspect of operation, the computing subsystem 110 can generatefracture pattern models based on an initial distribution for a fractureparameter. Each fracture pattern model can include estimated and/orsimulated locations of natural fractures of the fracture network 194.The computing subsystem 110 can refine the initial distribution and/orgenerate an updated distribution for the natural fracture parameterbased on comparing each fracture pattern model to microseismic eventdata for the subterranean region 193. The microseismic data may includedata collected from a first volume of the formation during a priorfracture treatment that was previously applied to the subterraneanformation at one or more first injection locations in the first volume(e.g., the injection location 196 a and/or another location). Asubsequent injection treatment can be designed based on the updateddistribution, and the subsequent injection treatment can be applied tothe subterranean formation through the well bore 192. In someimplementations, the subsequent injection treatment, which is designedbased on the updated distribution, is applied to a second volume of theformation at one or more second injection locations (e.g., the injectionlocation 196 b and/or another location). Microseismic data may becollected during application of the subsequent injection treatment, andused to predict fracture parameters for a third volume of the formation.In some cases, the technique of sequentially collecting microseismicdata from a volume of a formation, using the microseismic data topredict fracture parameters for another volume of the formation, andthen designing and applying a fracture treatment to the other volume ofthe formation based on the predicted parameters can be repeated insequence along the length of a well bore.

Some embodiments of a well system may be implemented with additionaland/or different variations. For example, in some cases, a well systemcan be implemented without an observation well or with more than oneobservation well. As another example, in some cases, a well system canbe implemented with more than one production and/or treatment wells. Asanother example, all or part of a computing subsystem can be integratedwith other features of a well system, all or part of a computingsubsystem can be implemented as a standalone system, and/or all or partof a computing subsystem can be used in connection with multiple wellsystems.

FIGS. 2A, 2B, and 2C collectively show an example of matching computersimulated fracture patterns with microseismic data. The matching, whichinvolves selecting or identifying fracture patterns that accuratelyapproximate the locations of the microseismic data, can be used torefine probability distributions used to generate the simulated fracturepatterns. As such, a generic or initial probability distribution can berefined, in some cases by an iterative process, to more accuratelyreflect the actual distribution of natural fracture parameters in aparticular geographic area, location, region, formation, or zone.

FIG. 2A is a plot of nine example fracture pattern realizations 202 a,202 b, 202 c, 202 d, 202 e, 202 f, 202 g, 202 h, and 202 i, eachgenerated based on initial probability distributions of fractureparameters. The initial probability distributions can include initialsample distributions generated based on well logs, outcrop data, and/orother types of data. The initial probability distributions may begenerated, for example, based on the techniques shown and described withrespect to FIGS. 7A, 7B, and/or 7C. The initial probability distributioncan include generic distributions of parameters for a selected type offormation, material, or region. A generic distribution can be definedbased on a distribution function. Examples of distribution functionsinclude a normal (or “Gaussian”) distribution, a log normaldistribution, an exponentially decaying distribution, a Poissoniandistribution, and others.

Each of the nine fracture pattern realizations in FIG. 2A contains majorfractures 206 a and 206 b, represented as bold lines. The majorfractures 206 a and 206 b are the same in each realization, because thelocations of those features are known with a high degree of certainty.As such, the major fractures 206 a and 206 b shown in FIG. 2A are notbased on a distribution of fracture parameters. The other features (theintermediate features) in each of the nine fracture pattern realizationsare based on distributions of fracture parameters because the propertiesof those features are not known with a high degree of certainty. Theintermediate fractures, represented as thin lines in the plots, varyamong the nine fracture pattern realizations because the locations (andother properties) of those features are determined by randomly samplingprobability distributions. For example, the fractures 208 a and 208 b infracture pattern 202 a do not appear in the other fracture patterns, andthe fractures 208 c and 208 d in fracture pattern 202 g do not appear inthe other fracture patterns.

In some embodiments, each realization of the natural fracture network isgenerated based sampling on values from probability distributions forfracture dip, fracture density, fracture direction, fracturepersistence, fracture aperture, fracture trace length, fracture centerpoint location, and/or fracture spacing. The fracture dip can indicate avertical angle of the fracture with respect to a horizontal orientation(or some other reference orientation). In some implementations, thefracture dip is initially assumed to be π/2, representing a verticalfracture. In some implementations, the fracture dip is initially assumedto be zero, representing a horizontal fracture. In some implementations,the fracture dip is initially represented by a normal distributioncentered about π/2, a log normal distribution centered about π/2, oranother type of distribution. The fracture direction can indicate anazimuthal direction (e.g., North, South, East, West, and combinationsthereof) of the fracture. In some implementations, the fracturedirection is initially assumed to be uniformly distributed in alldirections, from zero to 2π. In some implementations, the fracturedirection is initially assumed to have a single value, indicating thatall fractures have the same direction. In some implementations, thefracture direction is initially represented by a normal distributioncentered about a particular direction, a log normal distributioncentered about a particular direction, or another type of distribution.

The fracture persistence and fracture aperture can indicate the shapeand size dimensions of the fracture. In some implementations, thefracture persistence and aperture are initially assumed to be identicalfor all fractures, meaning that all fractures are assumed to have thesame dimension and shape. The assumed shapes can be rectangular,elliptical, triangular, circular, another regular shape, and/orarbitrary shapes. In some implementations, the fractures includefractures ranging in size from fractures that contact one square foot ofrock to fractures that contact thousands or millions of square feet ofrock, and/or fractures of other sizes. The fracture trace length canindicate the length (or in some cases, the half length) of the fracture.In some implementations, the fracture trace length is initiallyrepresented by a normal distribution, a log normal distribution, oranother type of distribution.

The fracture density can indicate an average number of fractures perunit volume in a subterranean formation or a portion of a subterraneanformation. Subterranean formations may exhibit a broad of fracturedensities. For example, a subterranean formation may include an averageof ten, one hundred, one thousand, or more fractures per cubic mile offormation. In some implementations, the initial fracture density of asubterranean formation is initially represented by a normaldistribution, log normal distribution, or another type of distribution.

The fracture spacing can indicate an average spacing between fractureswithin a fracture set in a formation. For example, in some formationsnatural fractures tend to form in sets, where each fracture in a set isoriented within approximately sixty degrees of each other. Someformations include multiple sets of fractures. For example, a formationmay include a first set of fractures having a primary orientation, whichmay be dictated by a maximum stress direction. A formation may alsoinclude a second set of fractures having a secondary orientation, whichis different from the primary orientation. The secondary orientation maybe separated from the primary orientation by more than sixty degrees.For example, the secondary orientation can be normal (orthogonal) to theprimary orientation. In some implementations, each set of fractures isinitially assumed to have a fracture spacing represented by a log normaldistribution, a normal distribution, or another type of distribution.

The fracture patterns shown in FIG. 2A are generated by samplingdistributions for fracture density, fracture trace length, and fracturespacing. In some implementations, a graphics processing unit can be usedto generate the natural fracture pattern realizations. Each examplefracture pattern realization shown in FIG. 2A may represents a plan viewof, for example, one square mile, two square miles, ten square miles, oranother area of a subterranean formation. The areal extent representedby a model may be a fixed or variable value. In some implementations,the areal extent is input by a user. In some implementations, the arealextent is determined based on the locations of microseismic events,based on a size of a reservoir or formation, based on sampling adistribution, and/or by another technique. For each realization, thecenter point of each non-major fracture is determined based at least inpart on sampling the fracture spacing, and the length of each non-majorfracture is determined based at least in part on sampling the fracturetrace length distribution. While nine realizations are shown in theexample, any number of realizations can be used. In some cases, hundredsor thousands of realizations are used. FIGS. 2A, 2B, and 2C showexamples of two-dimensional fracture models. In some implementations,three-dimensional fracture models may be used.

FIG. 2B is a plot of the nine example fracture patterns of FIG. 2A, witha map of microseismic event locations overlaid on each fracture pattern.The map of microseismic events is the same in each realization andoverlaid on each fracture pattern in order to compare the microseismicdata to each individual fracture pattern. The example microseismic dataincludes sixteen data points. For example, the data points 210 a, 210 b,and 210 c labeled in fracture patterns 202 a and 202 g are in the samelocation in all nine fracture patterns shown. While sixteen microseismicdata points are shown in FIG. 2B, any number of microseismic data pointscan be used. In some implementations, hundreds or thousands ofmicroseismic data points are used. In some implementations, themicroseismic data points that are plotted with and/or compared to thefracture patterns can include a subset of data points selected from alarger set of microseismic data points. For example, the larger set ofmicroseismic data point can include data points distributed over a rangeof vertical depths, and the selected data points can include a planarset of data points at (or within a certain range of) a particular depth.As a particular example, the first pane 502 of the graphical userinterface 500 of FIG. 5 shows microseismic data points distributed overa range of vertical depths, and the second pane 502 of the graphicaluser interface 500 shows a selected subset of the data points associatedwith a particular depth in the range.

Each microseismic data point can include information on a locationassociated with a microseismic event and information on a magnitudeassociated with the microseismic event. The information on the locationof the microseismic event may include spatial coordinates (e.g.,latitude, longitude, elevation, depth, etc.) that identify a location inthe subterranean formation where acoustic data indicates a microseismicevent occurred. Acoustic data gathered from one or more locations can beused to identify the location of the microseismic event, for example bytriangulation or another technique. The location and/or the magnitudemay be identified based on differences in time of arrival of thedetected acoustic signal, absolute or relative magnitudes of thedetected acoustic signals, waveform and/or relative phase differences ofthe detected acoustic signals, and/or other properties of the detectedacoustic signals. The location of each microseismic event is indicatedin FIG. 2B by the location of a data point on each fracture patternplot. The magnitude of each microseismic event is not represented in theexample plots of FIG. 2B. However, in some implementations, themagnitude of each microseismic event may be represented by a size of thedata point, a color of the data point, a shape of the data point, and/orin another manner. Each data point may additionally include informationon a time associated with the microseismic event. For example, the timeinformation may identify an absolute or relative time of occurrence ofeach microseismic event.

Each microseismic data point may additionally include information on anerror or uncertainty associated with the measured microseismic event.For example, there may be an error bar associated with the locationand/or the magnitude of each microseismic event. In someimplementations, the location of a microseismic event includes a rangeof possible locations representing uncertainty and/or errors in themicroseismic data. While error bars are not shown in FIGS. 2B and 2C, aplot or a map of microseismic events may include a graphicalrepresentation of error bars for microseismic event data. For example,in some instances, the location for each microseismic data point may berepresented as the center of a sphere or an ellipsoid, and the radius ofthe sphere can represent the uncertainty and/or error associated withthe measurement. In two dimensions, each microseismic data point may beanalogously represented as the center of a circle or an ellipse. Errorand/or uncertainty in the location and/or magnitude may be representedby another type of geometrical shape and/or in a different manner.

The plots of FIG. 2B can be used to compare the computer-generatedfracture pattern realizations with the microseismic data to determinewhich fracture pattern realizations correspond to the microseismic data.The comparison can be implemented using a variety of techniques. Asdiscussed with respect to FIG. 6A, the comparison can be fullyautomated, requiring little or no human interaction for comparing and/orselecting fracture patterns that correspond to the microseismic data.Also discussed with respect to FIG. 6A, the comparison can utilize humaninteraction and/or human feedback for comparing and/or selectingfracture patterns that correspond to the microseismic data.

As shown in FIG. 2B, the fracture pattern 202 a more accuratelyrepresents the microseismic data than the fracture pattern 202 g. Forexample, the microseismic data points 210 a, 210 b, 210 c, and othersare all relatively close to the fracture 208 a. By contrast, themicroseismic data points 210 a, 210 b, and 210 c are relatively far fromthe closest fracture 208 d. As such, the fracture pattern 202 a may beselected as an accurate representation of the microseismic data, and thefracture pattern 202 g may not be selected as an accurate representationof the microseismic data. FIG. 2C is a plot of the nine example fracturepatterns of FIG. 2B, showing which individual fracture patterns wereselected based on a comparison of the fracture pattern with the overlaidmicroseismic data. As shown in FIG. 2C, example fracture patterns 202 a,202 c, 202 d, 202 e, 202 h, and 202 i are selected as “matches” thatwell-approximate the microseismic data, and example fracture patterns202 b, 202 f, and 202 g are selected as “mismatches” that poorlyapproximate to the microseismic data. In various implementations,different criteria are used for comparing and selecting fracturepatterns. For example, in some implementations, pressure historymatching and/or other techniques can be used to compare and selectfracture patterns.

The selected fracture patterns 202 a, 202 c, 202 d, 202 e, 202 h, and202 i can be used to refine the initial probability distributions thatwere used to generate all nine of the fracture patterns shown in FIG.2A. For example, refined probability distributions for fractureproperties can be generated based on the selected fracture patterns, andnew realizations can be generated based on the refined probabilitydistributions. As a particular example, a new probability distributionfor fracture spacing can be generated based on the selected fracturepatterns 202 a, 202 c, 202 d, 202 e, 202 h, and 202 i, which results ina refined fracture spacing probability distribution. As anotherparticular example, a new probability distribution for fracture tracelength can be generated based on the selected fracture patterns 202 a,202 c, 202 d, 202 e, 202 h, and 202 i, which results in a refinedfracture trace length probability distribution. In some instances, arefined probability distribution for a fracture parameter can benormalized and/or combined with another probability distribution for thefracture parameter. For example, multiple field samples from one or moresubterranean regions can be combined and/or refined. Probabilitydistributions can be combined, for example, by summing and renormalizingthe probability distributions, or by another technique.

FIG. 3A is an example generic probability distribution for an examplefracture parameter. The horizontal axis represents a range of values fora fracture parameter (e.g., fracture dip, direction, length, density,spacing, aperture, center point location, persistence, etc.), and thevertical axis represents a range of probabilities. Each point on theline plot between the axes indicates the probability of a fracture in asubterranean formation having the corresponding fracture parametervalue. The example line plot in FIG. 3A is generated based on acontinuous log normal distribution. Generic probability distributionsmay include discrete distributions, and/or generic probabilitydistributions may have other functional forms, such as a log normaldistribution, a normal distribution, an exponentially decayingdistribution, a Poissonian distribution, and/or others. In some cases,the generic probability distribution can be refined based onmicroseismic data, so that the refined probability distribution moreaccurately represents the distribution of parameters in a particulargeographic region or formation. In some cases, a generic probabilitydistribution may be generated, for example, based on the techniquesdescribed with respect to FIGS. 7A, 7B, and/or 7C.

FIG. 3B is an example of an initial sample distribution for an examplefracture parameter. The horizontal axis represents individual values fora fracture parameter, and the vertical axis represents a range ofprobabilities. Each bar in the bar plot between the axes indicates theprobability of a fracture in a subterranean formation having thecorresponding fracture parameter value. The initial sample distributionis generated by randomly sampling the generic probability distributionof FIG. 3A. In some implementations, a distribution may be randomlysampled, for example, using a random number generator or a pseudorandomnumber generator. For example, software programs such as Mathematica(distributed by Wolfram Research), MATLAB (distributed by The MathWorks), and/or other programs may be used to randomly sample aprobability distribution. The initial sample distribution may representthe distribution of fracture parameters in one or more realizations of anatural fracture pattern model. In some implementations, an initialsample distribution is generated for each natural fracture patternmodel. In some implementations, an initial sample distribution isgenerated for multiple natural fracture pattern models. In some cases, arefined probability distribution can be generated from one or moreinitial sample distributions based on a comparison of microseismic datawith the fracture pattern models generated using the initial sampledistribution.

FIG. 3C is an example refined probability distribution for an examplefracture parameter. As in FIG. 3B, the horizontal axis in FIG. 3Crepresents individual values for a fracture parameter, and the verticalaxis represents a range of probabilities. Each bar in the bar plotbetween the axes indicates the probability of a fracture in asubterranean formation having the corresponding fracture parametervalue. The example refined probability distribution in FIG. 3C isgenerated by selecting values from the initial sample distribution inFIG. 3B. The values selected from the initial sample distribution andincluded in the refined distribution may be chosen based on a comparisonof a fracture pattern model with microseismic event data. For example, arefined probability distribution can be the output of an one or moreiterations of the refinement process described with respect to FIGS. 2A,2B, 2C, and 6A. In some cases, the refined probability distribution canbe a more accurate representation of the distribution of values of thefracture parameter in a particular geographic area, formation, field,layer, etc. In some cases, the refined probability distribution can befurther refined based on additional microseismic data (e.g., byiterating the refining technique), so that the refined probabilitydistribution more accurately represents a particular geographic area,formation, field, layer, etc.

Any of the probability distributions shown in FIGS. 3A, 3B, and 3C, aswell as other types of probability distributions can be used togenerate, and/or can be included in, a probabilistic earth model. Theprobabilistic earth model can be used to populate an initial geometricmodel of a subterranean formation. For example, populating the initialgeometric model may include generating a natural fracture pattern modelfor the subterranean formation, which can serve as a starting point forcomplex fracture propagation simulations.

FIG. 4A shows an example input geometric model 400 a, which includesdiscrete elements representing individual rock blocks of a subterraneanformation. An input geometric model may represent rock blocks defined bya natural fracture network in a subterranean formation. The geometricmodel 400 a includes seven discrete rock blocks of varying shapes andsizes. In some implementations of a geometric model, each rock block mayitself include one or more fractures. For example, each of the sevenrock blocks in the geometric model 400 a may include one or morefractures that are not shown in FIG. 4A. The example geometric model 400a is a simplified example, and a geometric model may generally includemany more discrete elements of arbitrary shapes and sizes. A geometricmodel may also include rock blocks of uniform shapes and sizes.

A geometric model may include information representing the boundaries,locations, orientations, shapes, and/or other properties of rock blocksin a rock formation. For example, information on a boundary of a rockblock may describe a shape of the rock block (e.g., square, triangular,elliptical, or an arbitrary shape) in any suitable manner. A shape of arock block may be represented, for example, by variables or datastructures that describe vertex locations, vertex angles, side lengths,arc lengths, arc angles, connectivity or lack thereof, and/or otherproperties. The information on the boundaries of a rock block mayinclude information on a location of the rock block and/or informationon an orientation of the rock block. A location of a rock block may berepresented by variables or data structures that describe one or morevertex locations, a center point location, and/or other types ofinformation. Location may be described with respect to a referencelocation, a location on a grid, with respect to other rock blocks,and/or in another manner. In some cases, a subterranean formation modelused for complex fracture simulation includes a geometric model thatdescribes boundaries of the formation. Information on boundaries,locations, orientations, shapes, and/or other properties of rock blocksmay include two-dimensional data, three-dimensional data, and/or othertypes of data. For example, a geometric model may represent atwo-dimensional plane in a formation, and the information on boundariesof rock blocks may include boundaries within the two-dimensional plane.As another example, a geometric model may represent a three-dimensionalvolume in a formation, and the information on boundaries of rock blocksmay include surface and/or edge boundaries within the three-dimensionalvolume.

One or more input geometric models can be generated based on aprobabilistic earth model. For example, a probabilistic earth model canbe used to generate a natural fracture pattern for a subterraneanformation, and the resulting fracture pattern can be used to define theboundaries, locations, shapes, and/or orientations of the rock blocksrepresented by the input geometric model. Thus, the boundaries of theelements of an input geometric model may represent a natural fracturenetwork in a subterranean formation. In probabilistic simulations,several input geometric models are generated by independently samplingprobability distributions of a probabilistic earth model. Each inputgeometric model can be used to simulate complex fracture propagation inthe formation represented by the geometric model; the simulation of eachgeometric model generates an output geometric model. The outputgeometric models can be analyzed individually and/or collectively topredict an outcome of an injection treatment, drilling, and/or othersubterranean activities. In some cases, an input geometric model can begenerated by another technique, such as a deterministic earth model.

A geometric model representing rock blocks of a subterranean formationcan be used with a discontinuum model to numerically simulate complexfracture propagation in the subterranean formation. The discontinuummodel can simulate internal and external forces acting on each rockblock represented by the geometric model. The simulated forces caninclude natural geological forces acting on the rock blocks independentof any drilling, production, or treatment activity. The simulated forcescan include forces generated in part or in full due to drillingactivities, production activities, and/or treatment activities. Suchsimulations can predict behavior of the rock blocks in response to themodeled forces. For example, the output geometric model can includecomplex fracture networks, including fractures that extend to a wellbore, along multiple azimuths, in multiple different planes anddirections, along discontinuities in rock, and in multiple regions of areservoir. The discontinuum model may simulate rotations, translations,deformations, fractures, and other types of responses of each individualrock block.

The geometric model 400 a can be used with the discontinuous deformationanalysis (DDA) technique, the numerical manifold method (NMM) technique,variations of these techniques, and/or other techniques to simulatecomplex fracture propagation in a subterranean formation. The DDAtechnique can be formulated with rock displacements as the unknowns, andthe technique can solve for the displacements by minimizing the energyof a block system for a given load. According to the DDA technique,translation, rotation, normal strain, shear strain, and possibly otherfunctions are permitted for each rock block. In some implementations,there is no tension between blocks and no penetration of one block intoanother. Rock block contact constraints can be numerically implementedwith “penalty submatrices” within a global stiffness matrix. A penaltysubmatrix can effectively insert a “spring” (i.e., a force model thatvaries linearly with position) or another type of force at the contactpoint between rocks, and the spring stiffness can be sufficient toprevent penetration.

In some implementations of the DDA technique, when a shear component offorce between rock blocks is greater than a frictional force between therocks blocks (e.g., friction according to Coulomb's law or anotherfunctional form), block sliding can occur along the contact. Modelingthe friction forces can be accomplished by modeling a spring forceparallel to a reference line along a contact. The DDA technique caninclude a variety of different block contact algorithms, sub-blockingalgorithms, and/or fracturing algorithms. An example block contactalgorithm uses an iterative Augmented Lagrangian technique for obtainingexact solutions for contact forces. The Augmented Lagrangian techniquecan utilize the spring model for block contacts, while adding aLagrangian multiplier. Implementing the Augmented Lagrangian techniquemay reduce or eliminate uncertainty associated with selecting anarbitrarily large spring constant to constrain block penetration usingthe penalty method. Other approaches utilize a sub-blocking algorithmthat subdivides each block and uses dual springs along and across eachinternal contact to enforce a “no-intrablock-displacement” constraint.Including the sub-blocking algorithm may allow tensile stresses to betransferred through sub-block contacts. A fracturing algorithm can alsobe added. An example fracturing algorithm uses a Mohr-Coulomb criteriato model block fracturing.

Along with a DDA-based approach or another approach, a discontinuummodel for simulating complex fracture propagation in a subterraneanformation may also incorporate fluid flow, fracture failure criteria,initiation tests for each block, intrablock fracture propagation models,and/or other features. A fluid flow model may include, for example,steady-state fluid flow in the fractures, unsteady-state fluid flow inthe fractures, sink/source terms, transient interporosity flow, andother types of flow.

As another example, the geometric model 400 a can be used with the NMMtechnique. Like the DDA technique, the NMM technique can be used tostudy the mechanical behavior of discontinuous rock masses. For example,the NMM technique can be used to analyze fissures, cleavages, joints,faults, and/or other features of rock blocks.

In some implementations, the NMM technique utilizes a two-layer model todescribe a physical rock block system. The two-layer model includes twomesh layers: a mathematical mesh and a physical mesh. The physical meshrepresents the physical boundaries and/or discontinuities of the rockblocks. For example, a physical mesh can be generated based on thegeometric model 400 a. The physical mesh may include, for example,information on fissures, cleavages, joints, faults, boundaries,locations, and/or other physical features of the rock block system. Themathematical mesh is a regular pattern or grid of geometric shapes(e.g., triangles, rectangles, etc.) that can be overlaid onto thephysical mesh. The mathematical mesh is larger than the physical mesh,and the size of the grid elements (i.e., the size of the geometricshapes that the mathematical mesh is composed of) can be determined, forexample, based on computational precision requirements, computationalaccuracy requirements, and/or other considerations. A covered manifoldmesh is constructed by overlaying the mathematical mesh onto physicalmesh and trimming the mathematical mesh at the boundaries of thephysical mesh. The covered manifold mesh, which includes the part of themathematical mesh that intersects the physical mesh, may be used tosimulate mechanical behavior of the rock block system, for example, tosimulate fracture growth, fracture dilation, fracture propagation, rockblock movement, and/or other phenomena.

In some implementations of the NMM technique, the covered manifold meshincludes nodes and elements that provide a framework for simulatingdynamics of the rock block system. The nodes and elements may beidentified based on the geometric shapes of the mathematical mesh grid.For example, when the mathematical mesh is a grid of triangles, eachtriangle can be an element and each corner of a triangle can be a node.Each node may contact (or “cover”) multiple elements. For example, whenthe mathematical mesh is a grid of triangles, each node may cover sixtriangular elements. The boundaries of the elements need not coincidewith the boundaries of the physical mesh. Instead, weighting functionsare used to connect the physical mesh with the mathematical mesh and totrack the physical boundaries of the rock block system. For example,when an element contains a discontinuity, thus dividing the element intotwo parts, the nodes covering that element can be duplicated, and oneset of the duplicated nodes can be used to track a first part of theelement, and the other set of duplicated nodes can be used to track asecond part of the element. The weighting function for a node can beused to identify which part of each element is tracked by the node.

To solve for displacements, the NMM technique may use a Simplexintegration technique. In some implementations, the Simplex integrationtechnique converts an integration over an arbitrary area to a sum ofintegrations over many grid elements (e.g., triangles, or another shape)of the arbitrary area, and each grid element is evaluated analytically.For example, the Simplex technique can be used to solve for first-orderlinear displacements of each node. The Simplex technique can be used tosolve for higher order (second-order, third-order, etc.) displacementsof the nodes. To model the kinematics of the rock block system, the NMMtechnique may utilize the same contact modeling approach as the DDAtechnique. For example, the NMM technique can model kinematics with theconstraints of (1) no tension between blocks and (2) no penetration ofone block into another. The NMM technique may also utilize theLagrangian multiplier approach, the augmented Lagrangian multiplierapproach, and penalty matrices that are used in connection with the DDAtechnique.

FIG. 4B shows an example output geometric model 400 b, which couldresult from a discontinuum model simulation of the geometric model 400 aof FIG. 4A. The example output geometric model 400 b includes a tensilefracture 402. A tensile fracture may occur in a formation when rockblocks fracture and/or separate. As such, a tensile fracture can besimulated in a geometric model when the forces modeled by the simulationcause elements of the geometric model to fracture or separate along afracture boundary perpendicular to the fracture plane.

FIG. 4C shows an example output geometric model 400 c, which couldresult from a discontinuum model simulation of the geometric model 400 aof FIG. 4A. The example output geometric model 400 c includes a shearfracture 404. A shear fracture may occur in a formation when a rockblock fractures or slides along a fracture boundary due to shear forces,acting parallel to the fracture plane. As such, a shear fracture can besimulated in a geometric model when the shear forces modeled by thesimulation cause one element of the geometric model to fracture or slidealong a fracture boundary parallel to the fracture plane.

An output geometric model can include other types of fractures andeffects that are not shown in the example output geometric models 400 band 400 c. For example, in some implementations, the elements of thegeometric model can fracture or split to form additional elements in thegeometric model, the elements of the geometric model can rotate and/ortranslate to change the orientation and/or position of the elements inthe geometric model; the elements of the geometric model can deform tochange the shapes of the elements in the geometric model, and/or thegeometric model can exhibit other effects.

Some embodiments and/or some aspects of the techniques and operationsdescribed herein may be implemented by one or more software programs orapplications running on a computing device configured to provide thefunctionality described. Such software programs and applications caninclude installed applications, executable files, interne applications,and/or other types of software tools. For example, a softwareapplication can be designed to analyze microseismic data, to identifyproperties of natural fractures (e.g., fracture density, fractureorientation, fracture direction, fracture trace length, and/or others),to generate and/or refine probability distributions of natural fractureparameters, to generate geometric models of natural and/or complexfracture patterns, to simulate one or more injection treatments in astochastic or deterministic manner, to predict rock blocks behaviorduring an injection treatment, to simulate resource production, and/orto perform other operations. In some instances, an application providesa graphical user interface that displays information to a user and mayalso allow a user to provide input. A graphical user interface can bedisplayed on a display device, such as a monitor, a display screen, oranother type of device. FIG. 5 shows an example screen shot 500 of agraphical user interface generated by a software tool for simulatingfracture propagation in a subterranean formation. Such numericalsimulation software can be used to analyze microseismic data and/or tosimulate complex fracture propagation over a broad range of verticaldepths, across vertical discontinuities, over a broad planar range,across horizontal discontinuities, encompassing diverse formations andcomplex fracture networks.

The example screen shot 500 includes a first pane 502 (shown on the leftin FIG. 5) and a second pane 520 (shown on the right in FIG. 5). Thefirst pane 502 presents an elevation view of the rock layers andmicroseismic event locations projected onto an xz-plane. In the firstpane 502, the vertical z-axis represents the vertical depth dimension inthe subterranean formation (e.g., distance below the surface, altitude,etc.), and the horizontal x-axis represents a horizontal dimension inthe formation (e.g., corresponding to a range of latitudes, a range oflongitudes, or a combination). The second pane 520 presents a plan viewof a rock layer of the subterranean formation and microseismic eventlocations projected onto the xy-plane. In the second pane 520, thevertical y-axis and horizontal x-axis both represent horizontaldimensions in the formation.

In the first pane 502, a vertical line plot 506 indicates changes inrock lithology in the formation. To the right of the vertical line plot506, locations of microseismic events are plotted. As in FIGS. 2B and2C, each microseismic data point can include information on a locationassociated with a microseismic event, information on a magnitudeassociated with the microseismic event, information on a time associatedwith the microseismic event, information on an error associated witheach microseismic event, and/or other information. For example, the datapoints 504 a and 504 b represent measured microseismic event locations.The first pane 502 presents paired lines 508 a and 508 b that indicate aselected horizontal layer of the subterranean formation. The second pane520 presents a plot of the microseismic events in the vertical rangebetween the paired lines 508 a and 508 b. For example, the data points504 c and 504 d in the second pane 520 represent two of the microseismicevent locations between the paired lines 508 a and 508 b. In someimplementations, a user can move (e.g., click and drag) one or both ofthe paired lines 508 a and 508 b to select a different layer and/oradditional layers of the subterranean formation.

The shape of each data point in the first pane 502 and/or second pane520 (e.g., data points 504 a, 504 b, 504 c, 504 d, etc.) indicates thestage of fracture treatment when the microseismic data corresponding tothat point was collected—data points having the same shape (e.g.,circle, triangle, left square, right triangle, diamond, etc.) werecollected during the same fracture treatment stage. In someimplementations, data points may be color coded, shaded, and/orotherwise configured based on the stage of an injection treatment thatproduced the events, based on the magnitude of the events, based on theerror associated with the events, and/or based on other information. Forexample, microseismic events recorded during a pad phase may be shadedwith a first color, and microseismic events recorded during aproppant-laden phase may be shaded with a second color. The center point526 in the second pane 520 may represent, for example, a well center fora vertical well, a fracture stage entry point center for a horizontalwell, and/or another reference location. In some implementations, areference line may also be presented in the first pane 502 to represent,for example, a well center for a vertical well, a fracture stage entrypoint center for a horizontal well, and/or another reference location,and microseismic events may be plotted in the xz-plane relative to thereference line.

In some implementations, microseismic events are recorded with respectto time, and a user interface control (e.g., a slider, or another typeof control) in the software tool may allow the microseismic events inthe first pane 502 and the second pane 520 to be animated. In someimplementations, a view and/or zoon control allows one or more of theplots presented in the user interface to be expanded, contracted,panned, and/or otherwise manipulated.

In the second pane 520, a solid rectangle 522 represents an area thatcontains a propagated fracture, for example, a fracture that wasinitiated and propagated through the formation during an injectiontreatment. The propagated fracture extends through the center point 526.The microseismic events in the solid rectangle 522 may be excluded whenanalyzing the microseismic data to identify natural fractures and/orproperties of a natural fracture network. A dotted rectangle 523represents an area that contains a natural fracture, for example, afracture that existed in the formation prior to the injection treatmentthat initiated and propagated the fracture in the solid rectangle 522.The line 524 a indicates a natural fracture. The location and otherproperties of the natural fracture may be determined, for example, basedon the times, the locations, the magnitudes, and/or other properties ofthe microseismic events in the rectangle 523. The line 524 b indicatesestimated locations of a second natural fracture. The estimatedlocations of the natural fractures may be used to estimate, calculate,and/or otherwise identify properties of a natural fracture network.

FIG. 6A is a flow chart of an example process 600 for refining aprobability distribution of subterranean fracture properties. Some orall of the operations in the process 600 can be implemented by one ormore computing devices. In some implementations, the process 600 mayinclude additional, fewer, and/or different operations performed in thesame or a different order. Moreover, one or more of the individualoperations and/or subsets of the operations in the process 600 can beperformed in isolation and/or in different contexts to perform one ormore of the disclosed techniques. Output data generated by the process600, including output generated by intermediate operations, can includestored, displayed, printed, transmitted, communicated and/or processedinformation.

At 602, an initial probability distribution for one or more fractureparameters is obtained. For example, the initial probabilitydistribution can be obtained by reading the initial probabilitydistribution from a memory, by receiving the initial probabilitydistribution from a remote device, and/or in a different manner. Thefracture parameters can include one or more fracture parameters for asubterranean formation. Example fracture parameters include orientation,direction, dip, length, depth, density, spacing, aperture, persistence,and others. The initial probability distribution can include a genericprobability distribution. For example, a generic distribution offracture lengths for shale may include a range of values of fracturelength observed in typical shale formations and a probability associatedwith each value in the range. The probability may indicate thelikelihood of finding a fracture having a given length in a typicalshale formation. The initial probability distribution can include aninitial sample probability distribution. For example, an initial sampledistribution of fracture lengths for a formation may include values offracture length observed in a particular formation and a probabilityassociated with each value. The probability may indicate the observedlikelihood of a fracture having a given length in the particularformation. The initial probability distribution may be generated, forexample, based on the techniques described with respect to FIGS. 7A, 7B,and/or 7C.

At 604, microseismic event data is obtained. The microseismic event datacan be obtained by reading the microseismic event data from a memory, byreceiving the microseismic event data from a remote device, and/or in adifferent manner. The microseismic event data may include information onthe measured locations of multiple microseismic events, information on ameasured magnitude of each microseismic event, information on anuncertainty associated with each microseismic event, and/or informationon a time associated with each microseismic event. The microseismicevent data may include microseismic data collected at an observationwell, at a treatment well, at the surface, and/or at other locations ina well system. The microseismic data (604) and the probabilitydistributions (602) may correspond to the same subterranean region,formation, or well, or the microseismic data (604) and the probabilitydistributions (602) may correspond to the different subterraneanregions, formations, or wells. In some examples, the initial probabilitydistribution is based on a treatment well data log, and the microseismicdata includes information collected during treatment and/or productionactivity at the treatment well.

At 606, multiple realizations of a fracture pattern realization aregenerated by sampling the probability distributions. For example, one ormore data objects defined in memory can represent each fracture patternrealization. A data object representing a fracture pattern realizationmay include values that represent the locations, sizes, shapes,connectivity, and other features of each fracture in the fracturepattern. Properties of each fracture in a fracture pattern realizationcan be determined based on randomly sampling the initial probabilitydistributions. For example, the length of a given fracture in a fracturepattern realization may be determined by generating a random number andusing the random number to select a value from an initial probabilitydistribution for the trace length parameter. As another example, thespacing of a set of fractures in a fracture pattern realization may bedetermined by generating a random number and using the random number toselect a value from the initial probability distribution for the spacingparameter. Each of the nine realizations in FIG. 2A is an examplefracture pattern model.

Each fracture pattern model generated at 606 can represent an estimatedor predicted natural fracture pattern for a subterranean formation. Thenatural fracture pattern realizations generated at 606 can be comparedto microseismic event data at 610. Alternatively or additionally, insome implementations, complex fracture propagation can be simulated ineach fracture pattern realization at 608 before the fracture patternsare compared to microseismic event data at 610. In either situation, at610, each fracture pattern realization, which may include a naturalfracture pattern and/or propagated complex fractures, is compared withthe microseismic event data obtained at 604.

The comparison at 610 can be implemented using a variety of differenttechniques. Two example techniques are shown in FIG. 6A. Othertechniques may also be used. In a first example technique for comparingthe fracture pattern models with microseismic event data, at 612, eachfracture pattern is mapped or plotted with the microseismic event data.For example, FIG. 2B shows nine fracture pattern models mapped withmicroseismic event data overlaid on each fracture pattern. At 614 (andas shown in the example in FIG. 2B), each fracture pattern model mappedwith microseismic event data can be presented (e.g., to a user) in agraphical user interface. Each fracture pattern model mapped withmicroseismic event data, or groups of fracture pattern models mappedwith microseismic event data, can be presented sequentially orconcurrently. Presenting the fracture pattern models mapped withmicroseismic event data may allow a user to visually inspect each map todetermine whether the microseismic data corresponds to the fracturepattern. At 616, selections of one or more fracture pattern models arereceived (e.g., from a user interface device, through the graphical userinterface, etc.). For example, the selections may indicate “matches,”which are fracture pattern realizations that accurately approximate themicroseismic data, or the selections may indicate “mismatches,” whichare fracture pattern realizations that poorly approximate themicroseismic data. For example, FIG. 2C shows an example of threeselected mismatches that have been identified, in the example shown, aspoorly approximating the microseismic data.

In some implementations, the comparison of the fracture pattern modelswith the microseismic data may be performed in an automated manner,without utilizing human interaction. In a second example technique forcomparing the fracture pattern models with microseismic event data, at618, distances between microseismic events and the nearest fracture ineach fracture pattern model are calculated. The distances can becalculated, for example, by a processor. In some implementations, foreach microseismic data point, a nearest fracture (i.e., a fracturenearest the microseismic data point) is identified in each fracturepattern model. A distance to the nearest fracture from the microseismicdata point can be calculated for each microseismic data point and foreach fracture pattern model. The calculated distances may account foruncertainty associated with the locations of the microseismic datapoints. In some cases, the calculated distances can be weighted based onthe magnitude of the microseismic event. For example, a larger magnitudemicroseismic event may be weighted more heavily than a lower magnitudemicroseismic event. The weighting can be linear, polynomial,exponential, logarithmic, a combination of those, and/or another type ofweighting. At 620, fracture pattern models are selected based on thedistances calculated at 618. Selecting fracture pattern models mayinclude determining for each fracture pattern model one or more indicesbased on the calculated distances. For example, the distances (or theweighted distances) may be summed (and/or combined in another manner)for each fracture pattern model to generate one or more indices. Asanother example, the largest or smallest distances (or weighteddistances) may be identified for each fracture pattern model to generateone or more indices. The index (or indices) for each fracture pattern(which may include the combined distances, selected distances, and/oranother type of index) can be used to determine whether the microseismicdata corresponds to that fracture pattern. For example, a fracturepattern model having an index greater than a threshold value can bedesignated a “mismatch,” and/or a fracture pattern model having an indexless than a threshold value can be designated a “match.” As anotherexample, the index for each fracture pattern can be compared to theindices for the other fracture pattern models, and a subset of thefracture pattern models can be selected based on the comparison.

At 622, the probability distributions are refined based on thecomparison. The refined probability distribution is generated based onthe results of comparing the generated fracture patterns with themicroseismic event data. The refined probability distribution mayrepresent the natural fracture parameter of the subterranean formationmore accurately than the initial probability distributions used togenerate the fracture patterns.

Refining the probability distribution for a given fracture parameter mayresult in an increase in the probability for certain values of theparameter and/or a decrease in the probability for certain values of theparameter. The particular probabilities that are increased and/ordecreased and the amount by which they are increased and/or decreasedmay be determined based on the selected fracture pattern models. Forexample, the refined distribution of fracture lengths can be generatedbased on the “matches” and/or the “mismatches” identified at 610. Forexample, the refined distribution can be generated according to thevalues of fracture parameters in each of the “matches.” In someimplementations, the values of fracture parameters in each of the“matches” becomes a sample, and the refined distribution is calculatedbased on the sample. In some instances, the refined distribution can berenormalized and/or combined with a distribution for a nearby field,well, or formation.

The refinement of a probability distribution may result in theprobability distribution more accurately representing the physicalproperties of the subterranean formation represented by the microseismicdata. A fracture pattern model generated based on the refinedprobability distribution may correspond more closely to the microseismicdata than a fracture pattern model generated based on the initialprobability distribution. In some cases, at 622, a probability will beincreased for values of a parameter occurring frequently in the fracturepattern realizations that accurately represent the microseismic data,and/or a probability may be decreased for values of a parameteroccurring infrequently in the fracture pattern realizations thataccurately represent the microseismic data. In some cases, a probabilitywill be decreased for values of a parameter occurring frequently in thefracture pattern realizations that do not accurately represent themicroseismic data, and/or a probability will be increased for values ofa parameter occurring infrequently in the fracture pattern realizationsthat do not accurately represent the microseismic data.

After the probability distributions are refined at 622, one or moreoperations of the process 600 may be iterated using the refinedprobability distributions as input probability distributions. Forexample, some or all of the operations 602, 606, 608, 610, and 622 andassociated sub-processes can be repeated in an iterative manner, furtherrefining the probability distribution upon each iteration. In somecases, such an iterative process can be repeated until an end conditionis satisfied. For example, the end condition can be based on theabsolute or relative amount by which the probability distribution isrefined in each iteration, the end condition can be based on the numberof iterations, and/or the end condition can be based on other factors.

At 626, the refined probability distributions are used. The refinedprobability distributions can be used for a variety of purposes. Forexample, the refined probability distributions can be incorporated intoa probabilistic earth model. A probabilistic earth model and/or therefined probability distribution can be used to generate an inputgeometric model for numerical simulations of complex fracturepropagation in a subterranean formation.

A probability distribution can be refined according to the process 600based on microseismic data in a first region or formation, and therefined probability distribution can be applied to simulations ofanother region or formation. As such, the refining process can producean output probability distribution that is extrapolated to a differentregion, zone, formation, field, or well site.

In some implementations, pressure history matching may also be used torefine a probability distribution for fracture parameters. In someimplementations, in addition to comparing fracture pattern models tomicroseismic event data, formation pressures observed during aninjection treatment are compared to formation pressures simulated usingthe fracture pattern model. For example, a fracture pattern models(e.g., “matches” or “mismatches”) may be selected based on a correlation(or lack thereof) between observed formation pressure and simulatedformation pressure. The observed formation pressure may be recordedduring an injection treatment, and the fracture pattern model may beused to calculate a model formation pressure. Selecting fractureproperty values that minimize the difference between the observedformation pressure and the model formation pressure may lead to animproved distribution of fracture property values. For example,comparisons of surface pressure, bottomhole pressure, closure pressure,and/or net pressure (i.e., the difference between bottomhole pressureand closure pressure) can be used. A pressure matching technique maypresent graphical comparisons to a user (e.g., Cartesian, log-log,and/or other plots of observed pressure and model pressure versus time)and receive input from the user based on the graphical comparisons. Apressure matching technique may include an automated technique thatcalculates differences between observed and model formation pressuresover time. In some implementations, an observed complex fracturegeometry may be compared to complex fractures in a fracture patternmodel. For example, fracture pattern models may be selected based onpressure history matching, microseismic data matching, propagatedfracture geometry matching, and/or other types of observed/model datamatching.

FIG. 6B is a flow chart of an example process 630 for simulating complexfracture propagation in a subterranean formation. The process 630 may beused for probabilistic simulation of complex fracture propagation. Forexample, the process 630 may include simulating complex fracturepropagation in multiple realizations of an input geometric model,thereby generating multiple output geometric models. Such probabilisticsimulations may be implemented by iterating one or more operations ofthe process 630. Each iteration may include a single geometric model, ormultiple geometric models may be simulated in parallel in each of one ormore iterations. Some or all of the operations in the process 630 can beimplemented by one or more computing devices. In some implementations,the process 630 may include additional, fewer, and/or differentoperations performed in the same or a different order. Moreover, one ormore of the individual operations and/or subsets of the operations inthe process 630 can be performed in isolation and/or in differentcontexts to perform one or more of the disclosed techniques. Output datagenerated by the process 630, including output generated by intermediateoperations, can include stored, displayed, printed, communicated,transmitted, and/or processed information.

At 632, a probabilistic earth model for a subterranean region isobtained. For example, the probabilistic earth model can be obtained byreading the probabilistic earth model from a memory, by receiving theprobabilistic earth model from a remote device, and/or in a differentmanner. A probabilistic earth model for a subterranean region describescharacteristics of the subterranean region and accounts for uncertaintyin some or all of the characteristics. The uncertainty may result fromimprecise or incomplete knowledge of the characteristics, inhomogeneityof the characteristics, and/or other sources of uncertainty. Theprobabilistic earth model may include probability distributions forcharacteristics of the subterranean region and/or rock formations in thesubterranean region. For example, probabilistic earth model may include(or be generated based on) the refined probability distributionsgenerated by the process 600 of FIG. 6A. The characteristics of thesubterranean region described by the probabilistic earth model mayinclude sizes and/or locations of rock formations in the region,composition of formation materials (e.g., shale, sandstone, carbonates,coal, mudstone, granite, and/or others), density of the formationmaterials (e.g., mass density, etc.), the amount void space in thematerial (e.g., porosity, etc.), the formation material's ability totransmit fluids (e.g., permeability, etc.), natural fracture propertiesof the formation (e.g., dip, direction, orientation, density, spacing,length, location, aperture, etc.), major faults in the region and/orformations in the region (e.g., location, size, orientation, etc.),and/or other characteristics.

A probabilistic earth model for a subterranean region may be generated,for example, based at least in part on data from one or more locationsand/or rock formations in the subterranean region, data from an outcropin the subterranean region, microseismic data from the subterraneanregion, seismic data from the subterranean region, pressure transientdata from the subterranean region, or open hole logging of a well borein the subterranean region. In some instances, a probabilistic earthmodel includes locations of major faults, which may be known withcertainty based on seismic data. In some instances, a probabilisticearth model for a first region may be generated based on open holelogging from adjacent wells, analog fields, and/or other regions andlocations. In some implementations, a probabilistic earth model caninclude data extrapolated from a different location. For example, datafrom an analog field may be extrapolated to another field to fit one ormore data points from a well log. The probabilistic earth model mayinclude additional and/or different information.

At 634, parameters of one or more injection treatments are obtained. Forexample, the parameters can be obtained by reading the parameters from amemory, by receiving the parameters from a remote device, and/or in adifferent manner. The injection treatment parameters may include, forexample, an injection location, a flow rate, pressure, volume, fluidcomposition, slurry concentration, information on proppants, informationon additives, and/or other data relating to one or more injectiontreatments. The injection treatment parameters may include, for example,injection locations, injection timings, and/or other information formultiple simultaneous or sequential injection treatments. The injectiontreatment parameters may relate to a pad phase, a proppant phase, afluid flush, and/or another aspect of one or more injection treatments.An injection treatment may involve injecting treatment fluid into theformation. For example, fluid can be injected at or below a fractureinitiation pressure for the formation, above at or below a fractureclosure pressure for the formation, and/or at another fluid pressure.

At 638, the probabilistic earth model is used to populate one or moregeometric models of a subterranean formation. In some cases, thegeometric models can be obtained by reading the geometric models from amemory, by receiving the geometric models from a remote device, and/orin a different manner. A data object in memory may be used to representthe geometric model. The geometric model may be, or may be included in asubterranean formation model. The geometric model may include atwo-dimensional, three-dimensional or another type of geometric modelthat can be used for simulating complex fracture propagation in thesubterranean formation. The geometric model includes multiple discreteelements that represent individual rock blocks of the subterraneanformation. A geometric model can include information on boundaries ofthe rock blocks, which may include estimated boundaries based on theestimated fracture locations. The size, shape, location, orientation,and other properties of the rock blocks, as represented by the geometricmodel, may be determined based on the probabilistic earth model (e.g.,the fractures, discontinuities, and/or other characteristics of thesubterranean formation). FIGS. 4A, 4B, and 4C show example geometricmodels. In some implementations, the geometric model may include anarbitrarily large or small number of discrete elements, and the elementsmay have arbitrary shapes, sizes, and other properties. In someimplementations, a geometric model may include rock blocks of uniformshapes and sizes. In some implementations, constraints may be imposed onthe number, shape, size, and/or other properties of the discreteelements. The constraints may be based on the probabilistic earth modeland/or practical considerations such as, for example, memory size,computational efficiency, processor speed, desired accuracy, numericalprecision tolerance, and/or others.

In the context of probabilistic simulation of complex fracturepropagation, each geometric model may be used for one simulation or formultiple simulations. Each geometric model may be generated by samplingthe probabilistic earth model. In some implementations, a geometricmodel may be generated, for example, by generating a natural fracturepattern model based on the probabilistic earth model and then using thenatural fracture pattern model to define the boundaries of the geometricmodel elements. Natural fracture pattern models may be generated asdescribed with respect to operation 606 in FIG. 6A and/or in a differentmanner. The probabilistic earth model may include probabilitydistributions for characteristics of a subterranean formation, and anatural fracture pattern model may be generated by randomly sampling oneor more of the probability distributions.

In an example implementation, the probabilistic earth model includesinformation on an areal extent of a rock formation (e.g., a 20 acreareal extent, a 500 acre areal extent, and/or other information on anareal extent of a rock formation), and the probabilistic earth modelincludes probabilistic information on fracture parameters of the rockformation, a shape of the rock formation, a thickness and/or changes inthickness of the rock formation, and/or other properties. By samplingthe probabilistic earth model for a given input geometric model,particular values for the natural fracture pattern, size, shape, andthickness of the rock formation are chosen, and the particular valuesare used to define an input geometric model.

At 640, output geometric models are generated by simulating fracturepropagation in each of the input geometric models populated at 638. Thesimulation can also be based on the injection treatment parametersobtained at 634 and/or other data. For example, the simulation mayinvolve simulating fluid pressure, fluid flow, proppant flow, and/orother physical phenomena in the subterranean formation during one ormore injection treatments. The simulated injection treatments mayinclude multiple sequential and/or simultaneous injection treatments.The fracture propagation simulation can be implemented using a varietyof different techniques. For example, complex fracture propagation canbe simulated using a DDA-based technique, an NMM-based technique, and/orother techniques. Complex fracture propagation simulation can emulate avariety of different subterranean events and properties. For example,simulations of complex fracture propagation can model forces that may beapplied to the subterranean formation by one or more injectiontreatments (e.g., based on the injection treatment parameters), forcesthat may be applied to the subterranean formation by fluid flow duringproduction, forces that may be applied to the subterranean formation byfluid flow during drilling activities, forces that may be applied to thesubterranean formation by natural geological events, and/or otherphenomena. In some examples, the discontinuum model is used simulateinitiation and growth of a two fractures in two different directionsduring an injection treatment. For example, a first fracture mayinitiate and grow in a first direction from a well bore, and a secondfracture may initiate and grow in a second direction from the well bore.The two fractures may initiate and grow in non-parallel planes. Thedirections of the fractures may be influenced by primary and secondaryfracture orientations in the formation.

The simulations at 640 can predict the locations and properties offractures that may form in the subterranean formation during a injectiontreatment. As such, the input geometric models can each represent aninitial condition of the formation, and the output geometric models (asgenerated and/or modified by fracture propagation simulation) can eachrepresent an intermediate or final condition of the formation. Theoutput geometric model may include complex fracture pattern modelsgenerated by a simulation. The complex fracture pattern models mayinclude networks of fractures that can extend, for example, to a wellbore, along multiple azimuths, in multiple different planes anddirections, along discontinuities in rock, and in multiple regions of areservoir.

In the example shown in FIG. 6B, the fracture propagation is simulatedby modeling, at 642, the forces acting on each rock block represented bythe input geometric model. The forces may include, for example, forcesof friction, shear forces, normal forces, external forces, forcesgenerated by steady state or unsteady state fluid flow, forces generatedby drilling activities, naturally generated forces, and/or others. Inthe example shown in FIG. 6B, the forces modeled at 642 can lead totranslation (644 a), rotation (644 b), and/or fracture (644 c) of any ofthe rock blocks of the geometric model. In some cases, the rock blocksmay deform, crack, and/or otherwise be modified during the simulation.In some instances, artificial fractures may be initiated and/orpropagated as a result of the modeled forces. In some instances, naturaland/or artificial fractures may be dilated as a result of the modeledforces.

In some instances, the output geometric models generated by thesimulation at 640 can be analyzed to generate output probabilitydistributions, at 652. For example, properties of the simulated complexfracture patterns in each geometric model can be summarized in outputprobability distributions. An output probability distribution may, forexample, identify probabilities of complex fracture spacing,probabilities of complex fracture length, probabilities of complexfracture size and shape, and/or others. For example, the outputgeometric models from the multiple realizations may be analyzed toidentify a most likely result of a given injection treatment; the outputgeometric models from the multiple realizations may be analyzed toidentify a least likely result of a given injection treatment; theoutput geometric models from the multiple realizations may be analyzedto identify a range of possible results of a given injection treatment,and in some cases, a probability associated with each possible result.Example results may include properties of the complex fracture network,properties of the complex fractures, and/or other properties. In aparticular example, analysis of the output geometric models can predicta probability of having a fracture that contacts a given amount of rock(e.g., a ten percent chance of having a fracture that contacts onehundred square feet of rock, a forty percent chance of having a fracturethat contacts eighty square feet or rock, etc.). As another example, theconnectivity and/or permeability of an output fracture pattern may beanalyzed.

In some instances, the output geometric models generated by thesimulation at 640 can be used to simulate (or otherwise calculate orestimate) production of resources from the subterranean formation at654. For example, a flow of resident fluids through the simulatedfracture pattern model may be simulated. In some cases, the productionsimulations may predict a volume, location, flow rate, and/or otherproperties of resource production through the fracture network.

At 656, injection treatment parameters can be modified and/or selected.The modification and/or selection of injection treatment parameters canbe based on the analysis of the output models (at 652) and/or thesimulated production (at 654). For example, injection treatmentparameters may be selected to improve and/or optimize production fromthe reservoir.

At 658, a injection treatment is applied to the subterranean formation.For example, the injection treatment may be applied as described withrespect to FIGS. 1B, 1D, and/or in another manner. Properties and/orsettings of the applied injection treatment can be set according to theinjection treatment parameters selected and/or modified at 656. Forexample, a flow rate, flow volume, flow pressure, slurry concentration,injection location, fluid composition, and/or other properties may bedesignated based at least in part on the results of simulations ofcomplex fracture propagation.

FIGS. 7A, 7B, and 7C show example techniques for generating probabilitydistributions. In some implementations, one or more of the operationsand/or example processes shown in FIGS. 7A, 7B, and 7C may be used togenerate an initial probability distribution representing one or morecharacteristics of a subterranean region. The characteristic representedby the probability distribution may include, for example, naturalfracture parameters, and/or other types of characteristics. In someimplementations, one or more of the processes shown in FIGS. 7A, 7B, and7C, or a similar process, may be used to perform all or part ofobtaining initial probability distributions at 602 in FIG. 6A. In someimplementations, one or more of the processes shown in FIGS. 7A, 7B, and7C, or a similar process, may be used to generate a probabilitydistribution included in the probabilistic earth model obtained at 632in FIG. 6B.

The example processes shown in FIGS. 7A, 7B, and 7C may include one ormore iterated operations and/or one or more iterated subsets ofoperations. Some or all of the operations in the example processes shownin FIGS. 7A, 7B, and 7C can be implemented by one or more computingdevices. Any of the selections made and/or identified in the exampleprocesses shown in FIGS. 7A, 7B, and 7C may be made and/or identified byan automated process and/or based on user input. In someimplementations, the example processes shown in FIGS. 7A, 7B, and 7C mayinclude additional, fewer, and/or different operations performed in thesame or a different order. Moreover, one or more of the individualoperations and/or subsets of the operations in the example processesshown in FIGS. 7A, 7B, and 7C can be performed in isolation and/or indifferent contexts to perform one or more of the disclosed techniques.Output data generated by the example processes shown in FIGS. 7A, 7B,and 7C, including output generated by intermediate operations, caninclude stored, displayed, printed, communicated, transmitted, and/orprocessed information.

FIG. 7A is a flow chart of an example process 700 for generating alinear fit for microseismic events. In some implementations, anothertype of fit may be generated for one or more of the microseismic events.For example, a non-linear curve fit may include a second-order (orhigher order) polynomial, a sinusoidal curve, a logarithmic curve,and/or other types of curves. The linear fits may represent estimatedlocations, shapes, lengths, and/or other properties of a fracture in asubterranean formation. In some implementations, some or all of theoperations of the process 700 may be carried out independent of userinput. In some implementations, one or more of the operations of theprocess 700 utilize input from a user. For example, some implementationsof the process 700 may require a user to identify, designate, and/ormodify linear trends in microseismic data.

At 704, microseismic event data for a subterranean region are plotted inan elevation view. For example, pane 502 in FIG. 5 shows an elevationview of example microseismic event data. The microseismic event data mayinclude data recorded during injection operations, productionoperations, and/or other operations. At 706, layers of the subterraneanregion are identified, and one or more layers are selected forevaluation. For example, the horizontal lines 508 a and 508 b in FIG. 5indicate a layer of the subterranean region selected for evaluation. At708, the microseismic events from the selected layer are plotted in aplan view. For example, in FIG. 5, pane 520 shows a plan view of themicroseismic events in the selected layer. At 710, the microseismicevents in the selected layer may be animated in the plan view plot. Forexample, two or more of the plotted points in pane 520 of FIG. 5 may beanimated based on the relative times at which the microseismic eventsoccurred. At 712, linear trends may be identified, for example, based onthe animation and/or other information. Microseismic eventsdemonstrating a linear trend are selected for regression.

At 714, a linear regression may be performed on the selectedmicroseismic events. The linear regression generates an equation for astraight line that fits the selected microseismic events. For example,linear regression may be performed by a least-squares technique and/orother types of regression techniques. In some implementations, themicroseismic events may be fitted to a non-linear curve using anappropriate regression analysis. For example, in some cases, themicroseismic events may be fitted to a polynomial curve (e.g., secondorder, third order, etc.) and/or another type of curve. At 716, a linerepresenting the output of the linear regression may be plotted throughthe selected microseismic events in the plan view. At 718, it may bedetermined whether all events (e.g., all events in the selected layerand/or all events in another subset of the data) have been fitted. Ifone or more microseismic events have not been fitted, the process 700may return to operation 710, and the operations may be iterated untilall microseismic events in the selected layer have been fitted. In theexample shown, if it is determined at 718 that all of the microseismicevents have been fitted, probability distributions may be generated at720. In some implementations, one or more of the example processes shownin FIGS. 7B and 7C and/or another process may be used to generate theprobability distributions at 720.

FIG. 7B is a flow chart of an example process 730 for generatingprobability distributions for fracture orientation and fracture tracelength. A similar process may be used to generate probabilitydistributions for one or more other fracture parameters (e.g., fractureaperture, fracture shape, fracture size, fracture dip angle, and/orothers). In some implementations, some or all of the operations of theprocess 730 may be carried out independent of user input. In someimplementations, one or more of the operations of the process 730 mayutilize input from a user.

At 732, multiple fracture sets are identified. For example, eachfracture set may include linear fits generated by the process 700 inFIG. 7A, where each linear fit represents an estimated fracturelocation. Typically, a fracture set contains fractures havingorientation angles within about plus or minus thirty degrees (±30°) ofthe mean orientation for the fracture set. Fracture sets can beidentified using stereo-projection techniques. In some implementations,fracture sets can be identified graphically from a map of microseismicevents and/or the linear fits. In some cases, there are a small number(e.g., 2, 3, etc.) of fracture sets, the fracture-dip angle is assumedto be π/2, and the linear fits are grouped into fracture sets. Aftergrouping the linear fits into fracture sets, the mean orientation anglefor each fracture set is calculated and compared to the orientationangle of each linear fit in the fracture set. If the orientation angleof a linear fit differs from the mean orientation angle for the fractureset by more than a limiting angle (±θ_(max)) the linear fits may beregrouped, and the process can be repeated until the orientation anglesof each linear fit are within the limiting angle (±θ_(max)) of the meanorientation angle for the fracture set. In some implementations, thelimiting angle (θ_(max)) is about thirty degrees (30°). Other values ofthe limiting angle may be used.

Probability distributions for fracture properties (e.g., fractureorientation, fracture trace length, fracture density, fracture spacing,and/or other fracture properties) can be generated based on eachfracture set. At 734, one of the fracture sets is selected for analysis.Each linear fit in the selected fracture set may include an equation ofan infinite straight line generated by a regression fit, such as theregression fit performed at 714 in FIG. 7A. In reality, fractures havefinite lengths. At 736, the fitted lines of the selected fracture setare truncated. The truncation points may be arbitrary, since thefractures are not observed directly. The truncation points for a linearfit may be selected based on the locations of the microseismic eventsthat were used to generate the linear fit, based on the error bars ofthe microseismic events that were used to generate the linear fit, basedon user input, for example, through a graphical user interface, based onclassical field outcrop-mapping fracture trace-length measurements,based on other information, and/or a combination of these. Additionallyor alternatively, the truncation points for a linear fit may be selectedand/or modified by adding or subtracting an arbitrary length from thelinear-trend ending events. The lengths of the truncated linear fits maybe used as an estimated fracture trace length for a fracture.

At 738, the orientation angle for each linear fit in the selectedfracture set is calculated. The orientation angle may be calculated froma reference orientation, for example, an East line or another referenceangle. At 740, a probability distribution of orientation angles isgenerated for the fracture set based on a histogram of calculatedorientations. For example, a histogram of orientation angles may begenerated, and the histogram may indicate, for multiple discrete rangesof orientation angle, the number of linear fits in the selected fractureset having an orientation angle in each discrete range. A probabilitydistribution function can be selected, parameterized, and/or otherwisegenerated based on the histogram. For example, the histogram maycorrespond to a normal distribution, log normal distribution, negativeexponential distribution, and/or another type of distribution. At 742,orientation angle statistics for the selected fracture set arecalculated. For example, the mean orientation angle, the standarddeviation of the orientation angle, and/or other statistics may becalculated based on the histogram and/or based on other data.

At 744, the line length for each truncated linear fit in the selectedfracture set is calculated. For example, the line length may becalculated based on the truncation points selected at 736, based on theerror bars, and/or based on other information. At 746, a probabilitydistribution of line lengths is generated for the fracture set based ona histogram of the calculated lengths. For example, a histogram of linelengths may be generated, and the histogram may indicate, for multiplediscrete ranges of line length, the number of truncated linear fits inthe selected fracture set having line length in each discrete range. Aprobability distribution function can be selected, parameterized, and/orotherwise generated based on the histogram. For example, the histogrammay correspond to a normal distribution, log normal distribution,negative exponential distribution, and/or another type of distribution.At 748, line length statistics for the selected fracture set arecalculated. For example, the mean line length, the standard deviation ofthe line length, and/or other statistics may be calculated based on thehistogram and/or based on other data.

At 750, it is determined whether orientation angle statistics and linelength statistics have been calculated for each fracture set. Ifstatistics have not been calculated for a fracture set, the process 730may return to operation 734, and the operations may be iterated untilstatistics have been calculated for all fracture sets. When statisticshave been calculated for each fracture set, the fracture densitydistribution may be calculated at 752. In some implementations, theexample process shown in FIG. 7C and/or another process may be used togenerate the fracture density distribution at 752.

FIG. 7C is a flow chart of an example process 760 for generating aprobability distribution for fracture density. A similar process may beused to generate probability distributions for one or more otherfracture parameters. In some implementations, some or all of theoperations of the process 760 may be carried out independent of userinput. In some implementations, one or more of the operations of theprocess 760 may utilize input from a user.

In some implementations, the process 760 may be performed after and/orin connection with the process 700 of FIG. 7A and/or the process 730 ofFIG. 7B. For example, the process 760 may initially obtain microseismicdata, fracture cluster data, and/or other data pertaining to asubterranean region. Fracture cluster data may include one or morefracture sets, such as the fracture sets identified at 732. Fractureclusters can be located in a stimulated reservoir volume, and at 764, avolume of the stimulated reservoir is calculated. The reservoir volumemay be calculated based on the spatial and/or planar extent ofmicroseismic event data, and/or based on other information. In someinstances, reliable probability distributions describing fracturecluster properties cannot be generated based on microseismic eventswithin a single stimulated reservoir volume, and analysis of fracturesets in multiple stimulated reservoir volumes may be required togenerate reliable probability distributions for the fracture clusterproperties.

At 766, a fracture set is selected. At 768, a fracture density for theselected fracture set is calculated. For example, the fracture densitymay be calculated as the number of fractures within the reservoir volumedivided by the calculated reservoir volume. At 770, if a fracturedensity has not been calculated for each fracture set, the process 760returns to 764, and the operations are iterated until a fracture densityhas been calculated based on all of the fracture sets. After a fracturedensity has been calculated based on all fracture sets, the process 760proceeds to 772.

At 772, it is determined whether there are fracture sets for any offsetwells in the reservoir. If there are no offset well fracture sets, theexample process 760 may proceed to 778, where fracture patternrealizations are generated. For example, in some implementations, thefracture pattern realizations may be generated as in operation 606 ofFIG. 6A, and/or fracture pattern realizations may be generated in adifferent manner.

At 772, if there are fracture sets for one or more other wells in thereservoir, the example process 760 may proceed to 774, where aprobability distribution of fracture density is generated based on ahistogram of fracture density for the reservoir. To calculate a fracturedensity distribution, the stimulated reservoir volumes corresponding tomultiple mappings in a horizontal well, the stimulated reservoir volumesfrom offset wells in the region, and/or other volumes may be combinedwith the treatment stimulated reservoir volume to prepare a fracture setdensity histogram. For example, a histogram of fracture densities may begenerated based on fracture sets for multiple offset wells in thereservoir. The histogram may indicate, for multiple discrete ranges offracture density, the number of fracture patterns having a fracturedensity in each discrete range. A probability distribution function canbe selected, parameterized, and/or otherwise generated based on thehistogram. For example, the histogram may correspond to a normaldistribution, log normal distribution, negative exponentialdistribution, and/or another type of distribution. At 776, fracturedensity statistics for the reservoir are calculated. For example, themean fracture density, the standard deviation of the fracture density,and/or other statistics may be calculated based on the histogram and/orbased on other data.

Any of the operations and/or processes shown in FIGS. 7A, 7B, and 7C maybe used in connection with a two-dimensional analysis, athree-dimensional analysis, and/or other types of analysis. For example,one or more of the described processes may be adapted forthree-dimensional analysis by identifying planar trends in athree-dimensional map of microseismic events. In some implementations,identifying and/or correlating data for multiple planes may also providedata for generating a probability distribution for fracture dip angle.

Some embodiments of subject matter and operations described in thisspecification can be implemented in digital electronic circuitry, or incomputer software, firmware, or hardware, including the structuresdisclosed in this specification and their structural equivalents, or incombinations of one or more of them. Some embodiments of subject matterdescribed in this specification can be implemented as one or morecomputer programs, i.e., one or more modules of computer programinstructions, encoded on computer storage medium for execution by, or tocontrol the operation of, data processing apparatus. A computer storagemedium can be, or can be included in, a computer-readable storagedevice, a computer-readable storage substrate, a random or serial accessmemory array or device, or a combination of one or more of them.Moreover, while a computer storage medium is not a propagated signal, acomputer storage medium can be a source or destination of computerprogram instructions encoded in an artificially generated propagatedsignal. The computer storage medium can also be, or be included in, oneor more separate physical components or media (e.g., multiple CDs,disks, or other storage devices).

The operations described in this specification can be implemented asoperations performed by a data processing apparatus on data stored onone or more computer-readable storage devices or received from othersources.

The term “data processing apparatus” encompasses all kinds of apparatus,devices, and machines for processing data, including by way of example aprogrammable processor, a computer, a system on a chip, or multipleones, or combinations, of the foregoing. The apparatus can includespecial purpose logic circuitry, e.g., an FPGA (field programmable gatearray) or an ASIC (application specific integrated circuit). Theapparatus can also include, in addition to hardware, code that createsan execution environment for the computer program in question, e.g.,code that constitutes processor firmware, a protocol stack, a databasemanagement system, an operating system, a cross-platform runtimeenvironment, a virtual machine, or a combination of one or more of them.The apparatus and execution environment can realize various differentcomputing model infrastructures, such as web services, distributedcomputing and grid computing infrastructures.

A computer program (also known as a program, software, softwareapplication, script, or code) can be written in any form of programminglanguage, including compiled or interpreted languages, declarative orprocedural languages. A computer program may, but need not, correspondto a file in a file system. A program can be stored in a portion of afile that holds other programs or data (e.g., one or more scripts storedin a markup language document), in a single file dedicated to theprogram in question, or in multiple coordinated files (e.g., files thatstore one or more modules, sub programs, or portions of code). Acomputer program can be deployed to be executed on one computer or onmultiple computers that are located at one site or distributed acrossmultiple sites and interconnected by a communication network.

Some of the processes and logic flows described in this specificationcan be performed by one or more programmable processors executing one ormore computer programs to perform actions by operating on input data andgenerating output. The processes and logic flows can also be performedby, and apparatus can also be implemented as, special purpose logiccircuitry, e.g., an FPGA (field programmable gate array) or an ASIC(application specific integrated circuit).

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital computer. Generally, aprocessor will receive instructions and data from a read only memory ora random access memory or both. The essential elements of a computer area processor for performing actions in accordance with instructions andone or more memory devices for storing instructions and data. A computermay also include, or be operatively coupled to receive data from ortransfer data to, or both, one or more mass storage devices for storingdata, e.g., magnetic, magneto optical disks, or optical disks. However,a computer need not have such devices. Devices suitable for storingcomputer program instructions and data include all forms of non volatilememory, media and memory devices, including by way of examplesemiconductor memory devices (e.g., EPROM, EEPROM, flash memory devices,and others), magnetic disks (e.g., internal hard disks, removable disks,and others), magneto optical disks, and CD ROM and DVD-ROM disks. Theprocessor and the memory can be supplemented by, or incorporated in,special purpose logic circuitry.

In some implementations, a processor may include a graphics processingunit (GPU) and/or a numerical processing unit (NPU). A GPU or NPU may beused to perform computations in parallel. For example, using suchdevices may improve the speed and/or reduce the time required forsimulating complex fracture propagation, for generating natural fracturepattern models, for predicting responses of rock blocks to forces, forrefining probability distributions, for generating input and/or outputsubterranean formation models, and/or for other computing tasks andoperations described herein. Some example GPUs include GPUs distributedby NVIDIA, which can be operated under the CUDA instruction setarchitecture. Alternatively or additionally, other GPUs may be used,such as, for example, GPUs distributed by ATI Technologies, Inc (ATI).

To provide for interaction with a user, embodiments of the subjectmatter described in this specification can be implemented on a computerhaving a display device (e.g., a CRT (cathode ray tube) or LCD (liquidcrystal display) monitor, or another type of display device) fordisplaying information to the user and a keyboard and a pointing device(e.g., a mouse, a trackball, a tablet, a touch sensitive screen, oranother type of pointing device) by which the user can provide input tothe computer. Other kinds of devices can be used to provide forinteraction with a user as well; for example, feedback provided to theuser can be any form of sensory feedback, e.g., visual feedback,auditory feedback, or tactile feedback; and input from the user can bereceived in any form, including acoustic, speech, or tactile input. Inaddition, a computer can interact with a user by sending documents toand receiving documents from a device that is used by the user; forexample, by sending web pages to a web browser on a user's client devicein response to requests received from the web browser.

A client and server are generally remote from each other and typicallyinteract through a communication network. Examples of communicationnetworks include a local area network (“LAN”) and a wide area network(“WAN”), an inter-network (e.g., the Internet), a network comprising asatellite link, and peer-to-peer networks (e.g., ad hoc peer-to-peernetworks). The relationship of client and server arises by virtue ofcomputer programs running on the respective computers and having aclient-server relationship to each other.

While this specification contains many specific implementation details,these should not be construed as limitations on the scope of anyinventions or of what may be claimed, but rather as descriptions offeatures specific to particular embodiments of particular inventions.Certain features that are described in this specification in the contextof separate embodiments can also be implemented in combination in asingle embodiment. Conversely, various features that are described inthe context of a single embodiment can also be implemented in multipleembodiments separately or in any suitable subcombination. Moreover,although features may be described above as acting in certaincombinations and even initially claimed as such, one or more featuresfrom a claimed combination can in some cases be excised from thecombination, and the claimed combination may be directed to asubcombination or variation of a subcombination.

Similarly, while operations are depicted in the drawings in a particularorder, this should not be understood as requiring that such operationsbe performed in the particular order shown or in sequential order, orthat all illustrated operations be performed, to achieve desirableresults. In certain circumstances, multitasking and parallel processingmay be advantageous. Moreover, the separation of various systemcomponents in the embodiments described above should not be understoodas requiring such separation in all embodiments, and it should beunderstood that the described program components and systems cangenerally be integrated together in a single software product orpackaged into multiple software products.

In the present disclosure, “each” refers to each of multiple items oroperations in a group, and may include a subset of the items oroperations in the group and/or all of the items or operations in thegroup. In the present disclosure, the term “based on” indicates that anitem or operation is based at least in part on one or more other itemsor operations—and may be based exclusively, partially, primarily,secondarily, directly, or indirectly on the one or more other items oroperations.

A number of embodiments of the invention have been described.Nevertheless, it will be understood that various modifications may bemade without departing from the spirit and scope of the invention.Accordingly, other embodiments are within the scope of the followingclaims.

1. A non-transitory computer-readable medium encoded with instructionsthat, when executed, perform operations comprising: receiving an earthmodel comprising a probability distribution for a property of asubterranean region; generating a subterranean formation model based onsampling the probability distribution for the property, the subterraneanformation model comprising information on boundaries of a plurality ofrock blocks of a formation in the subterranean region, the boundariesdefined by fractures in the formation identified by the sampling; andusing the subterranean formation model to simulate fracture propagationduring an injection treatment for the subterranean formation.
 2. Thecomputer-readable medium of claim 1, wherein the simulation of fracturepropagation predicts, for each of the plurality of rock blocks, aresponse of the rock block to forces acting on the rock block during theinjection treatment for the subterranean formation.
 3. Thecomputer-readable medium of claim 1, wherein the simulation of fracturepropagation generates an output subterranean formation model comprisinginformation on an updated boundary of at least one of the plurality ofrock blocks.
 4. The computer-readable medium of claim 1, wherein theearth model comprises information on at least one of: sizes of rockformations in the subterranean region; shapes of rock formations in thesubterranean region; locations of rock formations in the subterraneanregion; or mineral compositions of rock formations in the subterraneanregion.
 5. The computer-readable medium of claim 1, wherein the earthmodel comprises information on hydrocarbon reservoirs in thesubterranean region.
 6. The computer-readable medium of claim 1, whereinthe probability distribution comprises: a plurality of values for theproperty; and a probability for each of the plurality of values.
 7. Thecomputer-readable medium of claim 6, wherein sampling the probabilitydistribution comprises randomly selecting one of the plurality ofvalues.
 8. The computer-readable medium of claim 1, wherein the propertycomprises at least one of a fracture dip angle, a fracture direction, afracture shape, a fracture aperture, a fracture persistence, a fracturelength, a fracture location, a fracture density, or a fracture spacing.9. The computer-readable medium of claim 1, wherein the earth modelcomprises information on at least one of: lateral discontinuities withina rock layer of the subterranean region; vertical discontinuitiesforming multiple rock layers in the subterranean region; a primaryorientation of fracture sets in the subterranean region; a secondaryorientation of fracture sets in the subterranean region; or propertiesof formation materials in the subterranean region.
 10. Thecomputer-readable medium of claim 1, further comprising generating aplurality of additional subterranean formation models based onadditional sampling of the probability distribution, each additionalsubterranean formation model comprising additional information onboundaries of rock blocks of the formation based on the additionalsampling.
 11. The computer-readable medium of claim 1, the probabilitydistribution comprising a first probability distribution, the earthmodel comprising a plurality of additional probability distributions fora plurality of additional properties of the subterranean region, whereingenerating the subterranean formation model comprises sampling the firstprobability distribution and sampling each additional probabilitydistribution.
 12. The computer-readable medium of claim 1, wherein theinjection treatment comprises a fracture treatment.
 13. Acomputer-implemented method for simulating an injection treatment, themethod comprising: receiving an earth model for a subterranean region,the earth model comprising a probability distribution for a property ofthe subterranean region; generating, by data processing apparatus, asubterranean formation model based on sampling the probabilitydistribution for the property, the subterranean formation modelcomprising a plurality of elements representing a plurality of rockblocks of a subterranean formation in the subterranean region, eachelement comprising information on boundaries of at least one of the rockblocks, the boundaries defined by fractures in the formation identifiedby the sampling; and using the subterranean formation model to simulatefracture propagation during an injection treatment for the subterraneanformation.
 14. The method of claim 13, further comprising generating theearth model based on at least one of: data from an outcrop in thesubterranean region; microseismic data from the subterranean region;seismic data from the subterranean region; pressure transient data fromthe subterranean region; or open hole logging of a well bore in thesubterranean region.
 15. The method of claim 13, wherein using thesubterranean formation model comprises using the subterranean formationmodel to predict complex fractures in the subterranean formation, thecomplex fractures comprising at least one of: fractures that extendalong multiple azimuths in the subterranean formation; fractures thatextend in multiple planes in the subterranean formation; fractures thatextend in multiple directions in the subterranean formation; orfractures that intersect each other in the subterranean formation. 16.The method of claim 13, wherein the subterranean formation modelcomprises a first subterranean formation, the method further comprising:generating a plurality of additional subterranean formation models basedon sampling the probability distribution for the property; and using thefirst subterranean formation model and each additional subterraneanformation model as a plurality of input subterranean formation modelsfor simulating an injection treatment in the subterranean formation. 17.The method of claim 16, wherein the simulating generates an outputsubterranean formation model for each of the input subterraneanformation models.
 18. The method of claim 13, further comprisinggenerating the probability distribution by using microseismic data torefine an initial probability distribution for the subterranean region.19. The method of claim 13, wherein the subterranean formation comprisesa formation material, and the earth model comprises information on atleast one of a porosity of the formation material, a permeability of theformation material, a mineral composition of the formation material, acoefficient of friction of the formation material, a Young's modulus ofthe formation material, a Poisson's ratio of the formation material, acompressibility of the formation material, a fracture toughness of theformation material, a cohesive strength of the formation material, aBiot's constant of the formation material, or a pressure of fluidsresident in the formation material.
 20. A system for performing aninjection treatment, the system comprising: an injection treatmentcontrol subsystem adapted to control an injection treatment applied to asubterranean formation in a subterranean region through a well boredefined in the subterranean formation; the injection treatment beingbased on a simulation of fracture propagation in a subterraneanformation model, the subterranean formation model comprising informationon boundaries of a plurality of rock blocks of the subterraneanformation, the subterranean formation model generated based on samplinga probability distribution included in an earth model for thesubterranean region, the boundaries defined by fractures in theformation identified by the sampling.
 21. The system of claim 20,further comprising a computing subsystem that performs the simulation.22. The system of claim 20, further comprising a tool installed in thewell bore, the tool adapted to inject treatment fluid into thesubterranean formation based on information received from the injectiontreatment control subsystem.
 23. The system of claim 20, furthercomprising the subterranean formation, the subterranean formationcomprising at least one of shale, sandstone, carbonates, or coal. 24.The system of claim 20, wherein the well bore comprises a horizontalwell bore.
 25. The system of claim 20, wherein controlling the injectiontreatment comprises controlling at least one of a flow rate, a flowvolume, an injection location, a fluid property, a proppant property, ora slurry concentration.
 26. A method of treating a subterraneanformation, the method comprising: generating a model of boundaries of aplurality of rock blocks of a subterranean formation in a subterraneanregion based on sampling a probability distribution for a property ofthe subterranean region, the boundaries defined by fractures in thesubterranean formation identified by the sampling; designing aninjection treatment for the subterranean formation based on simulatingfracture propagation in the model; and applying the injection treatmentto the subterranean formation through a well bore in the subterraneanformation.
 27. The method of claim 26, wherein applying the injectiontreatment comprises injecting treatment fluid into the subterraneanformation at an injection pressure less than a fracture initiationpressure for the subterranean formation.
 28. The method of claim 26,wherein applying the injection treatment comprises injecting treatmentfluid into the subterranean formation at an injection pressure greaterthan or equal to a fracture initiation pressure for the subterraneanformation.
 29. The method of claim 26, wherein applying the injectiontreatment comprises injecting treatment fluid into the subterraneanformation at an injection pressure less than a fracture closure pressurefor the subterranean formation.
 30. The method of claim 26, whereinapplying the injection treatment comprises injecting treatment fluidinto the subterranean formation at an injection pressure greater than orequal to a fracture closure pressure for the subterranean formation. 31.The method of claim 26, wherein applying the injection treatmentinitiates a fracture in the subterranean formation.
 32. The method ofclaim 26, wherein applying the injection treatment dilates a naturalfracture in the subterranean formation.
 33. The method of claim 26,wherein the injection treatment comprises at least one of a pad phase ofa fracture treatment or a proppant-laden phase of a fracture treatment.34. The method of claim 26, wherein the simulating generates an outputmodel of updated boundaries for the plurality of rock blocks.
 35. Themethod of claim 34, wherein designing the injection treatment comprisesusing the output model to simulate production of resources from thesubterranean formation.